Significant Advancements in Numerical Simulation of Fatigue Behavior in Metal Additive Manufacturing-Review

Abstract

The concept of “Industry 4.0” encourages the use of automated manufacturing processes and the use of advanced technological systems. Some of the most fundamental needs of the Fourth Industrial Revolution can only be met with the help of additive manufacturing. However, the mechanical behavior and reliability of additive-manufactured components are hardly recognized. This paper provides a systematic review of metal additive manufacturing technologies, materials, lattice structures, and fatigue properties as well as the development of numerical simulations. The current state of development in metal alloys and the optimization of cellular structures were presented. In addition, this paper discussed the main challenges in numerical simulation methods, their validation with experimental results, and the limitations of commercial software used. Overall, this paper provides an overview of metal additive manufacturing as well as a survey of its simulation software development to optimize several parameters in industrial and academic research fields. The results were critically analyzed and provided a benchmark for future research and development.

1. Introduction

Additive manufacturing (AM) has recently emerged in the past two decades. It provides engineers with unparalleled design freedom, allowing them to build complex components without the need for specialized tools and reducing the cost of small-scale assembly methods [1]. Even the most complex CAD models with the necessary functionality may be manufactured, while this would be almost impossible with conventional manufacturing processes. The purpose of the AM process is to generate materials layer by layer [2], depending on the feedstock form (powders vs. wires) [3], feeding method (powder bed vs. blowing powder), energy source (Laser vs. Electron Beam), and materials (Titanium alloy, aluminum alloy, stainless steel, polymers, etc.). AM processes are offering new design flexibility for optimization techniques that are not limited by conventional production constraints [4]. Furthermore, the design freedom provided by AM techniques can result in a strength-to-weight ratio of up to 50%. Among the advantages of additive manufacturing is the high customizability of to-be-created components [5], lightweight components [6], less material waste, the possibility to mix varied technologies, and the simultaneous use of many materials to build a single product. Due to their high strength-to-weight ratio [7], AM components are widely utilized in the aerospace and automotive industries as well as in the biomedical [8] and construction industries. Continuous innovations and improvements in AM have also made it an indispensable technology in sectors like building and orthodontics [9]. Other improvements to bio-based materials and their mechanical, thermal, and chemical properties make it possible for AM to make parts that are long-lasting and environment friendly [10].

The Powder Bed Fusion (PBF) processes facilitate the construction of intricate lattice structures with specific physio-mechanical characteristics [11]. AM has made it easier and more productive to manufacture differently shaped structures with complicated geometries. These structures have significant uses in a variety of scientific domains, including biological and structural applications [12]. They are often encountered in several natural systems, such as the exoskeletons of beetles, the wings of butterflies, and other biological membranes [13]. Due to several limitations, the standard manufacturing technique cannot be used to create these structures due to their very complicated design and production process.

Due to its adequate and other mechanical qualities, the solid material structure is primarily employed in early industrial structural design. Although the solid material structure satisfies the design criteria to a considerable degree, it has several defects, including material waste, an inflexible design, a massive volume, and manufacturing challenges [14]. In addition, technological and scientific advancements have increased the demand for structural qualities. Currently, structural design in the industry places more emphasis on lightweight and performance. With the help of cellular structures, scientists can make and do things with low-cost, high-performance scientific materials [15].

Fatigue is the most common failure mode for AM materials and structural components. Indeed, a crack can be caused as a result of it. In cyclic loading situations, the applied stress might be uniaxial, biaxial, torsional, or fracture initiation and propagation far below the material’s yield strength [16]. These stresses are often associated with elastic deformation and not plastic deformation. Compared to their wrought counterparts, AM materials have a lower fatigue life. A shorter fatigue life may be attributed to factors such as flaws, residual stress, surface finish, geometry, size, layer orientation, and heat treatment [17]. The unique and complicated microstructure of AM alloys is one of the major factors in their reduced fatigue life. The three regimes of fatigue life may be distinguished: nucleation, small crack growth (less than 2 mm), and long crack growth [18]. Internal flaws such as gas porosities, Lack of Fusion (LOF) flaws, and surface flaws or roughness have been identified as the most significant fatigue damage locations, particularly in powder bed fusion components. Also, a lot of research has been conducted on how AM specimens behave when fatigue loads are applied to the Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF) areas, with a focus on how cracks start and spread from manufacturing defects.

Using sensitivity and parametric studies, it was possible to anticipate and study the fatigue behavior of the samples. The acquired findings demonstrate the great potential of a neural network that has been intensively trained to determine the effect of post-processing on the fatigue performance of Laser Powder Bed Fusion (LPBF) AlSi10Mg samples. By increasing the effect of shot peening on surface modification, surface hardness, surface compressive residual stresses, and the depth of compressive residual stresses, the fatigue life of a material with a constant stress amplitude was greatly increased [19].

Cellular lattice structures frequently push LBPF manufacturing processes to their technical limits. One might conceive that the functionality of a lattice structure could be increased by using a lattice structure with a hybrid form, in which the topology or relative density of the unit cells varies across the structure. These hybrid lattice structures may be categorized as functionally graded lattice structures and mixed topology lattice structures. Adaptive local characteristics may be attained via the use of hybrid lattice structures by taking advantage of the capacity to modify the geometry of certain regions of the structure to better adapt to local loads. Additionally, by altering the topology of certain regions of the lattice structure, features such as fluid flow pathways or heat transfer qualities may be adapted to the local environment [20]. The mechanical characteristics of various lattices have been examined by several scientists. The octa-truss lattice structure is more effective than similar-density foams constructed from the same material. The octa-truss lattice’s tensile strength, shear modulus, and stiffness suggest that this structure could be used instead of metal foams [21].

Therefore, non-destructive post-production testing is important for evaluating the real mechanical characteristics of manufactured components. When considering lattice components, the calculation of HCF life is a crucial factor. Numerical simulations may be a useful, non-disruptive technique to predict fatigue life. Nevertheless, the numerical characterization of the LBPF lattice is not simple since the original as-designed geometry might change significantly from the actual as-built geometry [22].

The prediction model based on the fault-tolerant design strategy, such as El-Haddad’s model [23], is often used to estimate the fatigue limit of AM materials. In this model, the defect is considered to be a fracture, and subsequently, Murakami developed a new parameter based on the predicted pore area to represent the fatigue limit as a function of porosity size and position [24]. Compared to the fatigue test of AM samples, this analytical method provides a realistic assessment of the endurance limit.

The stress-strain distributions served as inputs for the Fatemi–Socie (FS) damage model [25], which made it feasible to calculate the fatigue lifespan. In addition, the acting stresses on the interior pores were found to exceed 450% of the distant stress amplitude. The findings support a scale-bridging numerical solution based on microstructural damage that compensates for the short crack formation stage.

The study of fatigue strength of AM metals has focused on the effects of defects, as evidenced by the findings of several studies on the role of process-induced flaws in failure processes. The application of empirical models such as Kitagawa-Takahashi diagrams [26] and defect size parameterization techniques such as fractography and X-ray microcomputed tomography (µ-CT) has enhanced the interest in establishing a relationship between internal defect size and resistance to fatigue crack initiation. A recent study on defect analysis of defect distributions revealed that, even though 2D pictures may display the same patterns in defect creation, 2D representation cannot match the accuracy of 3D analysis in µ-CT, as shown by exhaustive statistical testing. The use of the threshold approach to measuring the impact of internal defects considers them from the outset as a notch or pre-crack, which contradicts the role of microstructure in slip band development near the pore [27]. In the presence of internal defects, especially at critical locations, it is widely acknowledged that the latter phase of fatigue life is marginal. Other efforts employ microcomputed tomography (µ-CT) to construct three-dimensional finite element models that imitate the shape of the interior pores, as has been portrayed progressively in the systematic review.

The mechanical behavior of porous AM biomaterials has lately attracted a growing amount of attention. Despite the availability of a substantial amount of information about the static mechanical characteristics of such biomaterials [28], this fatigue behavior is not yet fully understood. This is owing in part to the fact that a comprehensive examination of the fatigue behavior of these porous biomaterials is time-consuming and costly due to the vast number of parameters involved. It was claimed that a computational approach based on the finite element method might be used to predict the fatigue behavior of porous biomaterials, given the kind of repeating unit cell, unit cell diameters, and S-N curve of the material. The suggested method to predict the fatigue behavior of porous titanium alloy bio-materials created using Selective Laser Melting (SLM) on the rhombic dodecahedron unit cell is compared with experimental findings [29]. It was observed that these anomalies significantly reduce fatigue life, especially at lower stress levels.

Based on the aforementioned summary of the many difficulties impacting the AM components, it is apparent that there is a multitude of concerns. It indicates that the process must be adjusted to decrease the number of manufactured defects. To reduce the amount of trial-and-error experimental procedures, the option of using process design tools and improving the geometry of structures and characterization of materials may be of considerable benefit [30]. It is common knowledge that numerical modeling and simulation may lower production costs. Common to numerical techniques is the practice of doing calculations at specified nodes and then interpolating the results across the full domain as volume or surface [31]. To get a deeper understanding of the mechanical and operating principles of a process, numerical simulation would be a useful tool [32]. Most simulations use mesh-based methods and, in some cases, combined models. These include the Finite Element Method (FEM), the Discrete Element Method (DEM), the Finite Difference Method (FDM), and the Finite Volume Method (FVM). These methods are often used to solve boundary, initial, and eigenvalue problems [33]. FVM is used to examine the melt pool, pores, and surface contraction of structures [34]. ANSYS, ABAQUS, COSMOL, NASTRAN, MATLAB, AFGROW, and custom-built programs are examples of commercially available software used to solve problems [35].

From the previous literature review.

• Behzad et al. [36] criticized the mechanical behavior of SLM Ti-6Al-4V alloy in terms of microstructure, residual stress, and surface roughness. Changes in morphology during processing and heat treatment cause faults that affect fatigue behavior at different stages. Conclusions are reached on the pros and limitations of defect investigation approaches, including cost and time efficiency. Due to the expense of post-process defect-detecting tools like CT, in-situ AM techniques are gaining favor.
• Riccardo Caivano et al. [37] discussed the unmachined surface would cause earlier fatigue failure compared to machined samples. Final machining and polishing are critical for assessing Very High Cycle Fatigue (VHCF) strength. In addition to titanium and aluminum alloy, several other commercially available materials must be AM-produced. Study fracture initiation in AM-manufactured components to establish reliable design procedures and discover whether traditional design approaches may be used for AM materials.
• Shahriar et al. [38] discussed that horizontal builds offer better mechanical properties than vertical builds for SLM steel’s fatigue life. Improved temperature gradients, finer microstructure, and precise alignment of linear and planar defects in horizontal specimens increase mechanical properties. Uniaxial fatigue tests are common. Multiaxial loading affects SLM steel’s fatigue behavior. This gap may lead to a lack of knowledge of damage processes and an inability to anticipate industrial fatigue life.
• Carlos Romero et al. [39] investigated the fatigue and fracture properties of powdered titanium alloys. Powder-based approaches are more cost-effective than ingot-based processes for manufacturing equivalent or improved titanium alloys. Oxygen concentration affects Titanium alloy fatigue and fracture. Microhardness is sensitive to oxygen content; hence, its regulation is crucial.
• A P.Li et al. [40] study compares Ti-6Al-4V and conventionally produced components for uniaxial fatigue. The inability to consistently connect microstructure and defects to fatigue performance is a challenge for AM. To create and validate such models, more complete characterizations of defect populations and their spatial distribution, for example, for free surfaces, are needed, together with fatigue sample data from well-characterized specimens, for example, surface treatment. To ensure reliable and secure functioning, the certification framework must be aware of the application and the parameters listed.
• An Aref Yadollahi et al. [41] review examines fatigue characteristics and problems in laser-based AM metallic components. Several AM techniques use process-structure-property-performance (PSPP) correlation to reduce fatigue hazards. All of these variables must be considered since the fabrication parameters (process) of AM components affect their morphology (structure), which affects their mechanical properties and quality (performance).
• An Andrew. H Cheran et al. [42] study examines Electron Beam Melting (EBM) -made Ti-6Al-4V fatigue life. To establish fatigue parameters, the findings were compared to normally manufactured Ti-6Al-4V via AM EBM. According to the research, Hot Isostatic Pressing (HIP) and machining are the best ways to increase EBM part fatigue life.
• A review by Fei Cao et al. [43] focuses on AM Ti-6Al-4V. This study focuses on fatigue difficulties such as fatigue crack propagation, fatigue life, and fatigue behavior. It also quantifies the influence of faults on fatigue characteristics. In this research, SLM is preferred for manufacturing Ti-6Al-4V with enhanced fatigue performance. Wire Arc Additive Manufacturing (WAAM) has the greatest fatigue strength among AM methods. Existing research reveals that AM-manufactured Ti-6Al-4V is inadequate for fatigue-critical applications without post-processing consolidation, notably HIP, as well as surface machining and polishing.

Our findings show that the field is still in its infancy, with the majority of findings emphasizing the fatigue life of AM components. Over the last two decades, the quantity of scientific papers in AM has expanded significantly. A significant number of published review papers focus on experimental investigations of AM and technical insights. Also, there are so many factors that affect materials that it is very hard to make sure of their structure, process, and fatigue life. According to the existing literature, no systematic study or review of numerical simulation of fatigue behavior of AM components has been reported. In this work, we conduct a thorough analysis of the state of the art in Metal Additive Manufacturing (MAM) as provided in peer-reviewed scientific literature. The main goal of the research is to find out how numerical simulations of additively manufactured metals are getting better so that manufacturing defects can be fixed and the fatigue life of parts can be increased to meet market needs.

The organization of the paper is as follows. The classification of papers is described in Section 2. Next, results with materials, lattice structure, fatigue properties, material characterization, and numerical simulation with experimental results are described in Section 3. Finally, the summary of the manuscript with some conclusions is provided in Section 4 and Section 5.

2. Methods and Methodology

This report exposes a systematic literature review that was carried out in April 2022. The selection of published papers, following inclusion and exclusion criteria, is explained in Section 2.1.

2.1. Inclusion Criteria

To be eligible for inclusion in the review, publications must still report on specific aspects of fatigue in the additive manufacturing process as an alternative to subtractive manufacturing. Publications were evaluated if they were published in Scopus peer-reviewed journals or peer-reviewed conference proceedings, written in English, and documented as original research in engineering and material science, irrespective of the maturity of each published work. If an article did not fit the conceptual framework of the research (e.g., if it was a review or a position paper, or if it showed anything about fatigue that was relevant to the additive manufacturing process of metals), it was excluded.

2.2. Information Sources and Search Strategy

The following web databases were searched on 22 April 2022, to find possibly related publications: Scopus (524). Each data set was searched using the keywords “Title as Fatigue”, TITLE-ABS-KEY (additive manufacturing or selective laser), and TITLE-ABS-KEY (metal, aluminum, titanium, or steel). It was limited to document-type articles, and topic areas of engineering or topic areas of materials, as well as the English language. Using the export feature to get the results in CSV format and citing them with the open-source reference management tool Mendeley got the desired results.

2.3. Selection of Sources

The authors of this paper independently screened the titles and abstracts of all publications, excluding those without a title, abstract, or in a language other than English, records not corresponding to publications (such as book chapters, etc.), publications unrelated to additive manufacturing, and publications unrelated to the fatigue domain. When it was not possible to figure out any of the above, from the paper’s title or abstract, it was kept to look into further.

The reviewers examined their results and agreed on a consolidated publishing list. After the first screening of 250 articles, the reviewer independently and thoroughly examined the entire texts of the remaining publications. To get a consensus on a final selection of articles about fatigue in AM technologies within the engineering area. This final list was used to select and sort 107 articles into three groups: (1) numerical papers; (2) numerical and experimental papers; and (3) review papers.

2.4. Data Charting

The authors collaborated to construct a charting form for the data to decide which variables should be extracted. After that, each of them separately analyzed the results, and then the findings were reviewed. After the first screening, each manuscript on the list was given the following information:

2.4.1. Year of Publication

As shown by the database’s export of the citation.

2.4.2. Source Type

• Publication types considered include (a) journal papers and (b) conference proceeding papers.

2.4.3. Article Type

• (a) Numerical papers reporting fatigue in additive manufacturing processes (b) Numerical and Experimental papers on fatigue properties in additive manufacturing processes (c) Review papers.
• Each research paper includes the numerical simulation with the experimental investigation. If the paper has only experimental investigation, it is considered for future review work.

2.5. Classifications and Definitions

2.5.1. Selection of Sources

The Scopus database was used to obtain 650 papers. Following the first screening, 126 publications were deemed ineligible since they were neither full-length nor able to access certain journals. Thus, after the first screening of titles and abstracts, a total of 524 publications were procured for additional analysis. After excluding irrelevant publications that were unrelated to the search terms (additive manufacturing, metals), 274 papers were discovered. After deleting 167 publications, 99 papers, including experimental data validation with numerical simulations, and 8 papers containing reviews, remained. The 107 papers were kept for scoping review. Of the articles, 15% were considered for scoping review, and the number of papers published followed the trendline shown in Figure 1.

2.5.2. Paper Method: Numerical

A numerical paper is a paper where at least one new or original simulation or application of numerical elaboration of FEM data has been performed by the scholar, which is described in this paper. According to a study of data from 2013 to April 2022, it was retrieved 23 papers used numerical methods. In this instance, 14 papers were verified and compared with the old experimental data, while 9 papers were refined using the old data. According to the study of data, shown in Figure 2, relatively little numerical labor was performed in the early stages. However, numerical analysis is now exhibiting a steady increase.

2.5.3. Paper Method: Review

A literature review is when data existing in the literature are compared and NOR new/original simulation NOR new/original experiment are presented in the paper.

2.5.4. Paper Method: Numerical-Experimental

Experimental data obtained from conducting experiments and numerical data by FE simulation are presented in the paper. However, experimental data were used to validate or compare the simulation results (and not to be fine-tuned with the numerical solution). According to a data synthesis from 2013 to April 2022, 81 experimental papers containing numerical simulations were identified. In this study, numerical FE simulations were used to refine 32 experimentally investigated papers. In addition, 41 experimental papers were verified using numerical FE simulations. In Figure 2, the year-by-year trendline results in sustained growth and significant expansion in 2020 and 2021.

3. Results

3.1. Materials

By the systematic literature review, Figure 3 shows that titanium, aluminum, and stainless steel are the most used powder materials. In that, titanium occupied the top position. These metallic alloys provide great advantages in comparison to traditional manufacturing processes (e.g., machining, casting, and forming) due to their time-efficient, greater mechanical properties, and cost-effective process for manufacturing low to medium batch production of complex components [44].

3.1.1. Ti6Al4V Alloy

Ti6Al4V, the α-β titanium (Ti) alloy, is the most widely used titanium alloy in aviation and medical implants. As the implementation of the powder bed fusion process in the aviation sector advances, there is a growing need for resourceful and basic research to verify the strength and dependability of aircraft. Titanium’s increasing demand for biomedical devices, such as the knee, hip joint implants, jaw bone, and dental implants has stimulated the development of improved biomaterials [45]. Complex, titanium-based porous structures fabricated by AM technologies are attracting increasing attention. In addition to the life estimation, the Ti6Al4V alloy is the primary material of concern for design-critical components fabricated by powder bed fusion. The development in life expectancy demands that main components tolerate an extraordinarily large number of load cycles. This involves overcoming the obstacles of fatigue life and performance of the Ti6Al4V alloy [46].

3.1.2. Al-Si Alloy

Aluminum-silicon alloys are gaining popularity in aerospace and vehicle applications due to their high specific strength, ease of production (casting and additive manufacturing), and low thermal expansion coefficient. This alloy provides a good balance of strength and toughness and is used for components with thin walls and complicated geometries that are exposed to high stresses [47]. Aluminum alloys are widely used in aerospace, automotive, defense, energy, and many other industries. Challenging design requirements is those industries that call for the design of optimum lightweight structures and components that are capable of performing satisfactorily in their respective harsh service environments. AlSi10Mg alloy is a prominent hypoeutectic Al-Si alloy that is widely produced using the powder bed fusion technique because of its limited solidification range [48]. The high thermal conductivity and optical reflectivity of aluminum powder may require a greater amount of laser energy (powder) for the melting process, posing a significant difficulty in the LB-PBF of aluminum alloys [49].

3.1.3. Inconel 718 (IN718)

Inconel 718 (IN718), a nickel-based alloy, has been employed in aviation engines and gas turbines for the production of primary load-bearing components (e.g., blades and disks). To fulfill their aerodynamic purpose, these components have complicated geometries, and AM seems to be the only net-shape fabrication method capable of producing such complex parts [50]. However, for the aforementioned difficult applications, it is not always sufficient to achieve the requisite complicated form. Furthermore, they must have a desirable and dependable microstructure, mechanical properties, performance, and fatigue response that is equivalent to or greater than that of their wrought equivalents. The superalloy IN718 made of nickel was used as a model for making technical single crystals with the SEBM [51].

3.1.4. 316L Stainless Steel

316L is a chromium-nickel austenitic stainless steel with exceptional wear, corrosion resistance, weldability, ductility, and bio-compatibility, making it a unique alloy for marine, automotive, petrochemical, nuclear power plant, and biomedical applications [52]. In a number of these applications, the 316L SS components are intricately shaped and tailored. Consequently, AM is a potential component that may be subjected to repeated cyclic loads over the specified service lifetimes [53]. Traditional fatigue testing of 316L SS has been extensive; however, there appears to be a significant lack of knowledge on the fatigue behaviors of PBF 316L SS [54].

3.2. Lattice Structures

In early industrial structural design, the solid material structure is used primarily due to its adequacy and other material properties. Although the solid material structure satisfies the design requirements to a large extent, there are still numerous defects such as waste materials, an inflexible design, a large structural volume, and manufacturing difficulties. Furthermore, as science and technology advance, the requirements for structural properties have become more stringent. Currently, industrial structural design places a greater emphasis on light weight and excellent performance. For instance, in the aircraft industry, the structural design must not only fulfill the criteria of lightweight materials but also call for exceptional mechanical qualities. On this basis, low-cost and high-performance scientific materials may be created and accomplished. In the biomedical implant and aerospace sectors, the use of cellular lattice structures decreases the weight of the structure and enables the design application of lightweight and high strength.

Gibson and Ashby were the first to suggest the notion of a cellular structure. This cellular form featured open-cell and closed-cell foams, as well as honeycombs [55]. But lattice structure, which is also a type of cellular material, is different from foams and honeycombs mostly because of the shape, size, and properties of the unit cell [56].

In the past decades, Triply Periodic Minimal Surface (TPMS) porous structures have been the subject of study shown in Figure 4. The goal of geometric design is to make TPMS that are similar to some of nature’s most interesting porous structures. Porous TPMS structures are perhaps the most potential biomechanical manmade structures for bioengineering. For long-term use in a dynamic bio-skeletal system, the fatigue properties of AM porous materials are very important.

The fundamental cell is composed of trusses. Moreover, thin-walled TPMS and skeletal TPMS classes include TPMS-obtained elementary cells. Control must be exercised over the mechanical and thermal performance. TPMS structures are utilized as trusses, energy absorbers, heat exchangers, etc., to their competitive advantage [58]. To examine the behavior of a hybrid AM lattice structure under multiple loading directions, the strain rates, unit cell stacking order, and loading circumstances shown in Figure 5 were synthesized.

When hybrid lattice constructions are loaded in the transverse direction rather than the stacking direction, the maximum stress increases by up to 10% for all configurations. The flow stress fall after the peak was minimized when the structure was stressed in the transverse direction, hence minimizing the tensile failure of lattice struts.

3.3. MAM Technologies

A laser source is utilized to fuse metallic powder, making it one of the most commonly used AM techniques, which is shown in Figure 6, from the Systematic literature review. It is an automated method for producing complicated metal components straight from Computer-Aided Design (CAD) files by fusing metal powders. It does not require the removal of any binder, and in theory, any castable material can be used in the SLM process [60].

The Laser Powder Bed Fusion (LBPF) technique utilizes a high-density laser as a heat source to melt-fuse metallic powder into relatively close products with superior relative density and resolution. Modern laser sources like Nd: YAG, Yb: YAG, Yb: Fiber, and excimer gas lasers have substantially enhanced the precision and quality of AM components. This advancement in laser technology has increased the LBPF’s energy efficiency, allowing for appropriate laser power, scanning speed, layer thickness, hatch spacing, etc. to be used during sample printing. The enhanced LBPF version reduces macro-and microstructural flaws like balling, porosity, keyholes, and material evaporation in the final printed components. Reduced material flaws and the ability to print a wider spectrum of materials, such as copper, aluminum, and tungsten, would boost manufacturing efficiency. LBPF uses powder rather than wire material due to its higher laser penetration. Titanium alloys are expensive, and common ways to make them, like casting, forging, and machining, make them even more expensive [61].

However, proper process parameter selection is critical for operational success. Nonetheless, the strong temperature gradient caused by quick solidification following laser melting may result in residual strains and cracks. Typical flaws are pores caused by early powder contamination, evaporation, or local voids, following powder-layer deposition in the absence of fusion flaws. Defects are the primary problem regarding the fatigue performance of SLM components. Efforts are underway to optimize the SLM process parameters and to define acceptable thermo-mechanical post-sintering treatments [62].

WAAM feeds a wire at a regulated rate into an electric or plasma arc to melt the wire onto a substrate or previously placed layer. WAAM features a better material deposition rate, lower cost, and no powder handling requirements than laser or electron beam powder-based AM. Raw WAAM products have poor dimension and surface accuracy, requiring post-process machining. Material waste and machining costs are reduced for costly and difficult-to-machine high-strength titanium alloys.

Qualification and certification of service performance is a difficulty for using additive manufacturing to create safety-critical structural elements. Microstructure changes and process-induced residual stress alter WAAM-deposited components’ mechanical characteristics [63]. Widespread AM platforms have been proposed for repair based on DED technologies that utilize melting powder or wire feed with laser or EB energy sources to add material layer by layer to refurbish damaged components. DED technologies have advanced significantly for dimensional restoration [64]. However, fatigue-critical repairs are still in the development or qualifying phase, owing to the lack of performance data and poor confidence scatterplots. EBAM revealed encouraging static and uniaxial fatigue performance.

3.4. Fatigue Properties

According to the literature (Figure 7), HCF fatigue research published a maximum of 26 papers in the preceding year. Low cycle fatigue research has also improved compared to the previous years, a maximum of 6 papers were published. Some investigations with both HCF and LCF also demonstrate the depth of research in ortho implants. Therefore, conclusions based on the findings of the relevant literature suggest that HCF is the most significant research in industrial 4.0 [65].

A high degree of reliability and a large number of loading cycles make it important to comprehend and analyze the fatigue behavior of different materials in distinct fatigue regimes. This is exacerbated by the fact that 90% of component failure incidents in engineering applications are fatigue-related. For fatigue assessments, accelerated fatigue test techniques based on the premise of enhanced severity and decreased test duration have been widely utilized [66].

To find out how different SLM build orientations affect the fatigue properties of Ti6Al4V alloys, samples of in-situ fatigue and Rotating Bending Fatigue (RBF) bars were made using SLM methods with building orientations of 0°, 45°, and 90°, as shown in Figure 8. The S-N diagrams produced for each structure at various relative densities are depicted in Figure 8. It should be emphasized while evaluating the findings, that relative densities employed in the simulation are not identical to experimental densities. Considering this, there is a high level of concordance between simulation and experiment findings. In accordance with experimental findings, the predicted fatigue life of scaffolds reduced dramatically as the degree of stress increased.

Similar to typical solid materials, the S-N curves derived by numerical simulations and their experimental counterparts were linear on a logarithmic scale, as depicted in Figure 9.

Newman’s model for crack closing was utilized to correlate ΔK rate data from various stress ratios (i.e., R = 0.1 and 0.7). Figure 10a depicts the large-crack findings and the effective stress intensity factor for LPBF Inconel 718. These data are compressed into a narrow band with a restriction factor of α = 2.2 in the mid-rate regime. In the high-rate regime, some discrepancies are found between these two stress ratios, but these variances are predicted since the ΔK value at fracture is a function of R as the crack in the specimen expands toward failure.

The FASTRAN model accounts for these discrepancies using the two-parameter fraction criteria. The plasticity-induced closure approach under constant amplitude load capacity does not collapse the large-crack growth threshold data onto a unique effective stress intensity factor rate relation in the threshold regime when loading reduction methods are employed and the initial crack growth rate at the start of load reduction is excessively high [68]. This behavior is likely due to the relevance of fracture closure processes other than plasticity-induced closure during cyclic loading with load decrease. As a result, the high-stress (R = 0.7) data were used cautiously to assess the effective stress intensity factor rate in this regime. In the threshold regime, it was discovered that the real effective stress intensity factor data would lie at lower levels than those calculated using large-crack data. Based on the size of the flaw, the crack closure model and baseline effective stress intensity factor rate curve were used to estimate how the crack would grow from the size of the flaw when it first appeared until its failure.

The defect size is a significant geometrical characteristic that might influence fatigue life. Several investigations have found a reduced fatigue life for AM specimens with larger voids under the same testing conditions. Consequently, it is essential to investigate the variance in fatigue life of AM specimens based on void size [69]. In this respect, the range of probable fatigue life is computed for defective and non-defective construction specimens by varying the internal flaw size for a constant aspect ratio using the FASTRAN software. Figure 10b depicts the effects of void size on the fatigue life of defective and non-defective constructions. Acceptable fatigue curves developed for various builds of AM Inconel 718 suggest that understanding the statistical distribution of the defect size allows for a reasonable prediction of the scatter in the fatigue life of the AM material using appropriate fatigue analysis software such as FASTRAN. Importantly, the change in fatigue curves relative to the initial defect size also relies on the stress ratio, as seen in Figure 10 [70]. The fluctuation in fatigue life for a 100 µm change in initial flaw size for the test at R = −1 is not as substantial as that for a 12 µm change in the initial flaw size for the test at R = 0.1. This can be explained by the effect of plasticity-induced crack closure on fatigue life, which is more noticeable for the lower R-value.

In Figure 11, the estimated fatigue life at higher stress levels for as-built specimens is cautious. This uncertainty of fatigue damage may be attributable to the unique processes of fracture formation under various stress amplitudes, but the exact cause is unclear. For example, the size of the defect that acts as the starting site might vary depending on the degree of stress. In addition, fatigue failure may be caused by several occurrences of fracture initiation under larger stress amplitudes, which can alter the total crack development rate and the resultant predicted fatigue curve. To make fatigue curves for the non-defective build specimen with as-built surface polish, however, a single crack initiation site with constant geometry was tested at different stress levels.

To estimate the fatigue life in Equation (2) and the failure plane, Fatemi and Gates’ modification of the FS model is applied. The FS model was used because it gives accurate predictions for many kinds of metals, including AM metals, under a limited number of loading situations. The FS technique is a strain-equivalent model based on mode II/III failure. Where k is the correction factor relating the shear stresses seen in a pure torsion test to the highest shear strains observed in a tension-compression test. The parameter k measures the material’s sensitivity to normal stresses, as seen in Figure 12.

Using an equation, this parameter may be determined based on the fatigue life. As defined by Equation (2), the SWT model specifies the strain energy density as the damage parameter. The damage parameter takes normal strain and stress on the critical plane into account. This model is suitable for materials or circumstances that exhibit mode I fatigue failure mode.

$$\frac{{\mathsf{\Delta }\mathsf{\gamma }}_{\max }}{2}\left(1+\mathrm{k}{\frac{{\mathsf{\sigma }}_{\mathrm{n}}}{\mathsf{\sigma }}}_{\mathrm{y}}^{\max }\right)={{\mathsf{\gamma }}^{\prime }}_{\mathrm{f}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{{\mathrm{c}}_{\mathrm{o}}}+\frac{{\mathsf{\tau }}_{\mathrm{f}}^{\prime }}{\mathrm{G}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{{\mathrm{b}}_{\mathrm{o}}}.$$

(1)

$2{\mathrm{N}}_{\mathrm{f}}$ fatigue life cycle.

$${\mathsf{\epsilon }}_{\mathrm{a}}{\mathsf{\sigma }}_{\max }=\frac{{\left(\acute{{\mathsf{\sigma }}_{\mathrm{f}}}\right)}^2}{\mathrm{E}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{2\mathrm{b}}+\acute{{\mathsf{\sigma }}_{\mathrm{f}}}{\acute{\mathsf{\epsilon }}}_{\mathrm{f}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{\mathrm{b}+\mathrm{c}}$$

(2)

${\acute{\mathsf{\sigma }}}_{\mathrm{f}}, {\acute{\mathsf{\epsilon }}}_{\mathrm{f}}$ are the fatigue strength, and fatigue ductility, and, (b, c) are the exponents.

This model is suitable for materials or circumstances that exhibit mode I fatigue failure mode.

The connection between fatigue life and elastic strain range can be calculated by Basquin’s equation given by Equation (3).

$$\frac{\mathsf{\Delta }{\epsilon }_e}{2}={\epsilon }_e^a=\frac{\acute{{\sigma }_f}}{E} {\left(2N_f\right)}^b$$

(3)

${\epsilon }_e^a,$ is the elastic strain amplitude, fatigue strength coefficient, and fatigue strength exponent.

Figure 13 shows the fatigue life data for specimens with and without notches (b). Estimates from the FS and SWT models are shown as blue squares and green triangles, respectively. The SWT findings were not conservative and diverged even more with increasing fatigue life. A similar tendency was seen with the FS model, but with a considerably smaller divergence towards the nonconservative side. By increasing the size of the hole to 1 mm, the SWT findings become more conservative than those of the FS model.

Using the critical plane approach, the fatigue life and fracture development angles were computed. The fatigue life of the specimens with stress concentrators was more conservative. Compared to the FS model results, the SWT model’s behavior at lower load levels was less conservative. However, the modified FS model obtained better approximations than the SWT model, even when the critical plane on which fatigue damage had been obtained did not coincide with the appearance of cracks at high cycles. Compared to the FS model, the critical planes of the highest primary strain from the SWT model were closer to the experimental ones.

The SWT model seems to have a longer fatigue life. In contrast, the FS model showed the material is more suitable for the material at both low and high-cycle fatigue. According to the S-N data shown in Figure 14, the specimen with the greater yield stress (horizontal orientation) demonstrated a shorter fatigue life. The vertical yield stress is 16% less than the uniaxial fatigue strength [72]. The fatigue life and elastic strain also can be calculated by Basquin´s Equation (4).

$$\frac{\mathsf{\Delta }{\mathsf{\epsilon }}_{\mathrm{e}}}{2}={\mathsf{\epsilon }}_{\mathrm{e}}^{\mathrm{a}}=\frac{\acute{{\mathsf{\sigma }}_{\mathrm{f}}}}{\mathrm{E}} {\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{\mathrm{b}}$$

(4)

As shown in Figure 15 for AM Ti6Al4V, using this critical length while applying the TCD method [74] yields very excellent correlations between the notched and unnotched data within the scatter band of ±3. Figure 15 shows correlations between multiaxial notched and unnotched data for as-fabricated, surface-annealed Ti6Al4V specimens (c). While the data for other loadings are strongly linked within scatter bands of ±3, the torsion data deviate from the other data as life increases. This is due to the stair-stepping effect along the perimeter of the hole, which results in larger stress concentrations on the upper half of the notch’s perimeter, which may lead to a shorter lifespan under torsional loading. The total strain energy is expressed by the Coffin Manson Equation (5).

$${\mathsf{\epsilon }}_{\mathrm{a}}=\frac{\mathsf{\Delta }{\mathsf{\epsilon }}_{\mathrm{e}}}{2}+\frac{\mathsf{\Delta }{\mathsf{\epsilon }}_{\mathrm{p}}}{2}=\frac{\acute{{\mathsf{\sigma }}_{\mathrm{f}}}}{\mathrm{E}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{\mathrm{b}}+{\acute{\mathsf{\epsilon }}}_{\mathrm{f}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{\mathrm{c}}$$

(5)

The cyclic deformation modeling and fatigue lifetime prediction methods begin with estimating techniques for material properties that meet the required hardening criteria. Traditionally, parameter approaches are expensive since their implementation and evaluation demand a large lot of time and resources. The plastic strain [76] and material life span can be calculated by Coffin Manson Equation (6).

$$\frac{\mathsf{\Delta }{\mathsf{\epsilon }}_{\mathrm{p}}}{2}={\mathsf{\epsilon }}_{\mathrm{p}}^{\mathrm{a}}={\acute{\mathsf{\epsilon }}}_{\mathrm{f}}{\left(2{\mathrm{N}}_{\mathrm{f}}\right)}^{\mathrm{c}}$$

(6)

${\mathsf{\epsilon }}_{\mathrm{p}}^{\mathrm{a}},{\acute{\mathsf{\epsilon }}}_{\mathrm{f}},\mathrm{c}$ is the plastic strain amplitude, fatigue ductility coefficient, and exponent.

The Fatemi–Socie model is used to forecast the lifetime, and the simulation’s maximum shear stress is utilized to determine the longevity.

3.5. Material Characterization

Using SEM, AM Ti-6Al-4V polished and etched metallurgical samples of SLM Ti-6Al-4V manufactured with optimum processing settings were analyzed for their porosity. The microstructure in the proximity of the gas pores was identical to the overall microstructure, suggesting that the cooling rates in the vicinity of the holes were not significantly different from the overall cooling rates. The internal flaws are shown in Figure 16. Based on the pictures, it could be assumed that the flaws have a perfect spherical or oblate spherical geometry.

The LCF life of Ti6Al4V alloy samples at various strain amplitude levels decreases as the strain amplitude level increases. Fatigue fractures initiate on the surface in Figure 17 and a network of microcracks promotes crack propagation under continuous cyclic stress.

The failure mechanism under multiaxial loading may be affected by the parameters of the post-fabrication heat treatment; for example, tensile failure was seen for the annealed condition and shear failure was detected for the HIPed specimens, comparable to the axial and torsion loading situations. Multiple HIPed specimens showed that they were ductile by having small cracks around the failure crack.

During the testing of several annealed specimens, it was noticed that fracture orientation occurred in an unanticipated direction. Further study revealed that this may be the result of the combination of multiple internal flaws. These findings are for the combined in-phase axial-torsion test on the annealed material. Two LOF defects developed independently of the surface and then combined to produce the failure fracture. One of the cracks reflects mode-I orientation, and the other shows mode-II orientation. Because AM metals have a lot of flaws on the inside and these flaws interact with each other when a fatigue crack spreads, it is possible to see fractures in unexpected directions.

The micro truss collapses gradually, starting with the fatigue failure of one of the ligaments. Typically, this occurs at the ligament node contact. The failure points of a failed micro truss are highlighted in Figure 18 even though failure often occurred at ligament-node interfaces, failure at the margins of the micro truss happened via the 1⁄4 nodes (rather than at the ligament-node interface).

As an example, Figure 19 depicts a fragmented piece of a CUB S specimen after heat tinting. The SEM was used to examine the shattered portions of the fatigue specimens to have a better understanding of the damage process. Almost always, the fatigue fracture propagates in a single plane. Due to the larger struts of the first plane of unit cells, the specimen often separates from the bulk component. This behavior differs from that reported in compressive-compressive fatigue testing, in which the broken struts are arranged along a 45° inclined plane under stress. The fatigue crack propagates throughout the specimen section when successive struts fail as a result of cyclic loading until the stiffness of the structures is reduced enough to halt the test.

The fatigue crack in the segment of the strut often occurs from surface imperfections and not from inside pores [80].

3.6. Numerical Simulations

The FEM is the technique of subdividing all systems into their constituent components or elements. In the majority of research, FE-simulation findings are compared to experimental values; nevertheless, the FEA technique varies greatly across studies, and a systematic approach to constructing the model is often not documented. Additionally, it must be emphasized that strut-based porous structures are often categorized according to their deformation mechanics. The structure is considered to be dominated by bends. If the struts bend or buckle under compressive force; alternatively, for certain porous architectures. Some struts may support an axial tensile load during compression, and these constructions are categorized as stretch dominant [81]. It is unknown how deformation mechanics and other kinds of cellular geometries would impact convergence, precision, and the reliability of findings as compared to physical-mechanical testing at a minimal computing cost [82]. This will first be performed on structures dominated by bending, with the expectation that it can be extended to structures dominated by stretching, stochastic structures, and graded structures.

An FE-model was constructed by ANSYS to determine the stress and strain values around the concentrator. Figure 20 shows the highest primary stress distribution at the surface of the specimen around the drilled hole for the B2 test at the maximum load point.

The research scientific method is a sequence of processes that follows a pattern. Generating high-quality CAD models. Generate lightweight designs that can be produced by additive manufacturing technology. The printed AM components may be a cylindrical, dog-bone specimen, a Compact test (CT) specimen with a solid material, or porous structures for the multiaxial testing. The AM manufactured specimen were admitted for post-processing such as machining, polishing, shot peening, laser peening, sandblasting, and HIP process to improve the fatigue life of the materials. Then, the post-treatment process leads to different multiaxial testing. The machine operates in force control, whereby the force was calculated by considering the load-bearing cross-section that excludes the area of the channels. Consequently, the applied force was lower for samples with higher numbers and larger diameters of channels, respectively, to consider an equal nominal maximum stress amplitude for all samples tested.

For building the models and solving the governing equations, the ANSYS implicit solver was utilized. For modeling the struts in the microscale part of the model, Timoshenko beam elements with three integration points (BEAM189 in ANSYS) were employed, while eight-noded brick elements (SOLID185 element type) were employed for discretizing the macroscale portion of the method.

The fatigue failure pattern anticipated by numerical modeling for all structures is shown in Figure 21. The figure describes the displacement contour in the direction of loading. The geometry of the failure pattern may reveal information about the formation of cracks and the distribution of macro stress in scaffolds. The development of shear bands indicates that shear forces may not be the primary failure mechanism at the macro scale. In contrast, cyclic tensile stress owing to bending moment played a crucial part in the fatigue failure mechanism of the microscale strut. The experimental findings demonstrated that the fatigue failure surface was 45° angled concerning the loading direction. Again, there was a strong correlation between numerical modeling and experimental findings.

The value of the stress concentration factor for four distinct pore geometries was determined using an elastic FE model under uniaxial loading conditions and a Poisson’s ratio of 0.324. It demonstrates that Poisson’s ratio influences the stress concentration factor in three-dimensional geometry. As shown in Figure 22a, the stress concentration factor increases as the distance between the pore and the free surface decrease below the pore diameter. Figure 22b,c illustrates the stress distribution for subsurface pores under unit stress application. Lastly, the stress concentration factor was also high for an internal oblate spherical pore. This shows that the shape of the pore also has a big effect on the local stress concentration factor.

The distribution of the Crossland fatigue indicator parameter (FIP) for three geometries is shown in Figure 23. In terms of FIP localization, it is evident that Schwartz cells substantially localize FIP in their central zone, but gyroids do not. In the latter instance, the FIP localizes to a single cell branch. In contrast, the diamond cell provides for a more uniform distribution of the stress field over the whole volume of the cell. It is surprising to see that the two cells with the highest FIP localization have the lowest fatigue resistance.

During the computational area of numerical simulations, initial material conditions are considered to be loaded for elastic and plastic deformation. As seen in Figure 13, a Von-Mises stress contour map has been constructed to comprehend the stress distribution throughout the specimen. A sectional view (Figure 24b) gives a better understanding of the essential stress fluctuation near the fracture tip along the direction of the crack’s thickness. The critical zone (Figure 24b) in the fracture area of the CT specimen indicates that crack growth started near the crack tip. When it exceeds the fracture toughness value, it becomes unstable. So, it seems likely that the results of the simulation and the experiment are similar.

The XFEM is an efficient approach for resolving fracture mechanics issues, namely the elastic-plastic crack development behavior for a wide range of engineering materials. Figure 25a depicts the results of a simulated tensile test, with a magnified view showing the crack initiation, propagation, and ductile fracture at the alloy gauge section. At the commencement of necking, clusters of micro-voids and interfacial non-connected cracks collect towards the secondary phase, resulting in the production of small-sized cracks. Furthermore, as plastic straining increases, these fractures spread and are primarily responsible for the specimen’s central weakening at the necking regime.

This phenomenon is well modeled by the XFEM simulation seen in Figure 25a. It is obvious from the data that the plasticity is accommodated by plastic straining in the tensile curve, and this phenomenon of ductile tearing is also visible in the magnified image of the tensile failed specimen. The stress-strain curve is compared to the graph in Figure 25b. Excellent agreement exists between the simulated and empirically determined curves.

Figure 26 depicts the dispersion of von Mises equivalent stresses in the notch region for nominal axial, torsion, and combined in-phase axial-torsion loads. The nominal von Mises stress was applied to the models in a manner that produced a surface equivalent stress of one MPa. As can be observed, the region of the notch with the greatest stress changes according to the loading circumstances. The SCF under axial and torsional stresses is around 3.0 and 3.5, respectively. Based on the cross-sectional area, the SCF for torsion load was found by dividing the local equivalent stress by the nominal shear stress.

Independent of the load level, the corners of the lattice construction acquired the highest amounts of stress and strain. A component of fatigue resistance is negatively impacted by the existence of a stress raiser in a structure. Any sharp corners on the surface of a component may enhance its susceptibility to fatigue failure. So, any improvement to the structure’s design, especially at the sharp corners, makes both its static strength and its cyclic strength better.

3.7. Numerical Simulation Validation with Experimental Results

During the computational examination, the crack route is also traced as a force vs. COD trace curve, as illustrated in Figure 27a, and compared to the empirically observed curve. The actual and simulated curves have proven to have a high degree of congruence. The arrow mark is shown in Figure 27a. indicates the maximum load attained during the application of load about the COD opening. It is rather intriguing that the calculated curve has proportionally greater load levels than the observed data points. Due to the failure to account for the change in stiffness that happened during fatigue pre-cracking during the experimental assessment of fracture toughness, a discrepancy was observed.

To examine the critical impact of defect sizes on specimen fatigue performance, Murakami’s parameter, the square root of defect projected area acquired from RBF specimen fracture surfaces, was utilized to characterize SLM sample defect sizes, and numerical analysis was performed. The defect size distribution features of SLM Ti6Al4V specimens in 0°, 45°, and 90° construction directions are shown in Figure 27b, based on the Weibull distribution with three parameters. The majority of 0° samples (square root of area) were less than 100 m, which was much smaller than the values for 45° and 90° samples, which were 154 µm and 141.2 µm, respectively. Based on the Weibull distribution function, 99.99% of SLM defects (square root of area) were predicted to be smaller than 147.4 µm for 0° samples, 186.9 m for 45° samples, and 169.2 µm for 90° samples. For LM 45° and 90° Ti6Al4V samples, the fatigue performance was worsened and the fatigue limits were lowered when the size of the defects was larger.

• FEA vs. Neuber’s model

If the porosity is considered a notch, Neuber’s approach can determine local stress and strain. Neuber’s method was utilized to determine local stress and strain in three pore geometries. Figure 28 compares the FE model findings to Neuber’s in terms of computed local strain amplitude under applied stress amplitudes between 200 MPa and 560 MPa with applied stress ratios of 0.1, −0.2, and −0.5. Local strain from the FE model matched Neuber’s technique for lower plastic strains. Neuber’s approach was more conservative for greater plastic stresses than the FE model. Neuber’s technique allows complicated algorithms to better approximate non-linear material behavior.

Figure 29a shows combined experimental vs. FASTRAN predicated fatigue life for both materials under all loading conditions. For the multiaxial loading conditions, the implemented crack growth-based approach resulted in accurate estimates of the fatigue life of notched AM specimens [85], as compared to the experimental results.

As shown in Figure 29b, the experimentally determined elastic modulus of the specimens is relatively similar to the value expected by FE calculations based on CAD models. Most likely, the differences between the experimental and FE results are due to flaws in the geometry of the specimens, such as strut oversizing due to the way they were made, strut cross-section variation along the strut-axis, and strut dislocation.

Comparing experimental and numerical findings Figure 30. Consequently, owing to the negative value of the stress exponent (b), the fatigue life reduced as the cyclic load increased. In contrast to the actual findings, all computational models predicted a longer lifespan for the lattice abutment.

In comparison to the actual findings, the Soderberg model produced the most accurate forecast of fatigue life among the three techniques of mean stress correction. Although the majority of experimental data received from fatigue testing of metals fall between the Goodman and Gerber curves, the adoption of the Soderberg adjustment as the most accurate correction does not necessarily contradict the aforementioned tendency. As the most accurate adjustment, the Soderberg correction does not necessarily contradict the stated trend. It must be mentioned that the bulk of experimental fatigue testing is performed in a laboratory. Multiple investigations have shown that the presence of stress raisers may significantly reduce the fatigue characteristics of a component. This impact will be considerably more evident in EBM-produced lattice structures. EBM-manufactured products have a greater amount of surface roughness as one of their distinguishing qualities [87]. Low-thickness struts are the weakest connections in the porous structure and are susceptible to significant plastic deformation. A tight match between experimental data and numerical findings of a more cautious Soderberg adjustment reveals the effects of the aforementioned parameters on fatigue life. When designing a component based on its yield strength, the Soderberg relationship is applied. It indicates that, under cyclic stresses, the specified lattice structure seldom undergoes plastic deformation. Under torsion and multiaxial stresses (Figure 31), horizontal specimens have more fatigue strength at 2 million cycles (run-out limit) than vertical specimens, however, under uniaxial loads, vertical orientation demonstrates greater fatigue strength than horizontal orientation.

There is a significant difference between the projected outcomes and the actual data, as seen in Figure 32. Moreover, just one set of data falls inside the 1.5 error zone. The predicted outcomes exhibit significant dispersion. An ML framework based on sensitive features and CDM is suggested to forecast the fatigue life of L-PBF-built AlSi10Mg samples to achieve high-precision and high-reliability fatigue life prediction of AM components. The extraction of sensitive features reduces the effect of feature causality on the prediction performance of the ML model. Also, the CDM-based life is used as physical information to describe how AM components break down under different levels of stress.

4. Discussion and Future Trend

Following the background discussed in the literature review, the justifications for the current state-of-the-art proposal have been developed based on the research potential noticed after classifying the papers. The purpose of these prospects is to direct the research’s actions so that they are correctly initiated. Our findings show that field is still in its infancy. The research maturity of the papers included in the literature review suggests that cellular lattice structures in additive manufacturing are still an emerging field. The yearly distribution of related publications supports this finding, showing that research activity from 2019 increased at much higher rates than the general position in the same field.

In the first 5 years, research is greatly focused on only Titanium alloys, and now for the past 3 years Inconel 625/718, stainless steel, Al alloys, and Maraging steel are emerging for industrial applications. However, Titanium alloys are still increasingly used as Porous lattice structures in biomedical implants, and aerospace applications due to their lightweight, cheaper cost, and strength-weight ratio [89]. Powder bed fusion is employed with laser and electron beam also increased two times than normal use by its applications for manufacturing small components. DED technology is preferred by the manufacturer for larger components and for repairing worn-out parts. The numerical method by FE-simulations remains constant but the utility of open-source software increases steadily over the commercial software of its cost. The validation of experimental papers with numerical analysis has grown over only the experimental investigation method.

According to the systematic study, data of SLM, EBM, and DED, Ti-6Al-4V shows that unpolished specimens performed poorly with no measurable effect of any postprocessing, while the fatigue strength was increased by a factor of 2–3 for the specimens tested with a polished surface. In polished specimens, heat treatment (without HIPing) did not show any significant improvement in fatigue performance as compared to non-heat-treated specimens [90]. After identifying the critical locations and stresses of a part using FEA, the performance of AM components may be enhanced by fine-tuning the processing parameters and design parameters during production. This technology is very cost-effective and time-saving for the AM process [91].

The optimization methodology proposed was able to find an efficient geometry, and fulfill the design requirements [92]. The optimization was proved to be efficient by optimizing the volume and the mass of the component was 12.53% of the initial domain. The stiffness-to-mass ratio was almost six times higher than the initial value.

The residual stresses resulting from the AM process have a substantial influence on fatigue. Therefore, it must be considered during the design phase of components vulnerable to cyclic stresses [93]. To reduce the residual stress upon processing, the build platform was heated to 200 °C. Moreover, before machining the cylinders were stress-relief, and heat-treated at 800 °C for 2 h., under a vacuum atmosphere [94]. By examining SEM imaging that shows a sub-surface fusion fault [95]. It is between many-particle boundaries and cracks to the surface. Indeed, unmelted powder forms between two-particle boundaries. Material anomalies indicate the prevalent porosity type and process-inherent flaws in fatigue specimens. It has been investigated that experimental fatigue results were estimated according to a probabilistic model. The resulting S-N curves were approximately the same with the scatter bands being nearly coincident [96]. In other words, the laser speed effect is negligible and no influence is found on the fatigue lifetime of Ti-6Al-4V specimens. In addition, the HIP process consists of heat treatment of AM parts under high pressure. It can reduce the number of residual stresses as well as the size of defects [97]. Application of the HIP treatment to evaluate its influence on multiaxial fatigue behavior of Ti-6Al-4V materials [98].

To achieve an HCF life estimate using the Finite cell method (FCM) with an implementation particularly tailored to operate on µ-CT images to conduct numerical studies on the as-built geometry [99]. CDM is used to estimate fatigue life using randomly distributed subsurface hydrogen pores compared with a homogeneous model [100].

CAD methods may create varied geometric characteristics, however, most performance control research uses uniform TPMS structures [101]. TPMS tissue engineering scaffolds or implants are highly addressed in recent research works. TPMS scaffolds provide mechanical, mass transfer, and cell growth benefits. As said, TPMS has promise in other interdisciplinary fields. Few mechanical studies use graded TPMS [102]. Too much study focuses on TPMS mechanical performance. Different materials’ compression capabilities are explored. More research is required on TPMS heat and mass transmission, particularly heterogeneous and multiscale TPMS [103].

The design of cell topological shapes is still insufficient, and most of the literature is still studying the existing structures. The performance of cell structure is directly related to lattice structure, so it is necessary to design cell topology with a special performance. In the topology optimization of lattice structures, most of the research still focused on the strut sizes. The single optimization is not conducive to the design of lattice structures. Only from point of view of optimizing struts, the lattice structures cannot meet the specific requirements [104].

Deep learning, as one machine learning-based approach, was suggested to be an excellent tool for forecasting fatigue behavior and studying the effects of post-treatments on additively constructed materials when combined with pre-training methods such as stacked auto-encoder [105].

5. Conclusions

Even though AM continues to show promise for large-scale production of complicated geometric components, their mechanical behavior and, therefore, their reliability are hardly recognized. This provides a challenge for the complete implementation of the AM technique in diverse engineering, biomedical, and dental-implant applications. The hybrid lattice structure is the future material to maintain a balance between porosity (for bone ingrowth) and mechanical properties, graded TPMS lattice structures meet the demands of bone-in growth and high-stress regions for bearing high loads. Further tuning the morphological parameters and strut diameter for multidirectional will improve the strength and high-energy absorption with a systematic porosity distribution over implants. Using a hybrid gradient TPMS lattice structure for bio-implants will alter the porosity, cell size, and pore size separately with more flexible and smooth transitions of mechanical properties [106].

Based on these, numerical models have been developed to enhance the fatigue resistance of components in an attempt to address this challenge. Cumulative findings indicate that numerical simulation results closely reflect experimental outcomes. This will decrease the enormous expense and duration of experiments [107]. Several pieces of research reveal that enhancing the surface polish and adjusting the surface geometry can increase the fatigue life of components. Formulating numerical simulation models based on the structure-process-fatigue properties (SPFP) method for AM components would be the first step in limiting prototypes, decreasing experimentation, optimizing the design, and enhancing the component’s dependability. FEA can be used to make models that can be used to figure out the fatigue life of any part with a complicated shape. Lattice structures are future industrial materials. Because of its high performance and unique properties, topological optimization of porous lattice structures should be explored for biomedical and industrial materials. The experimental inquiry will concentrate on gaining an understanding of the typical behavior of porous structure materials.