In this study, the axial stress distribution in STS inserted perpendicular to the face of mass timber members (CLT and glulam) under varying moisture conditions are numerically modelled. The specimen configurations shown in
Figure 1 and moisture content changes shown in
Table 1 are numerically modelled using the commercial ABAQUS FEA software [
7]. As seen in
Figure 1, screws of nominal outer diameters of 8 mm and 13 mm were inserted into the broad face of CLT and glulam of different sizes. The test program included two mass timber products. There was glulam made from douglas fir-larch of stress grade 16c-E and spruce-pine-fir (SPF) CLT of stress grade V2 [
8]. The initial moisture condition shown in
Table 1 represents the moisture content of the CLT or glulam during STS installation, and the final moisture content represents the moisture condition of the CLT or glulam due to variations in the surrounding environment. For the sake of simplicity, this study considered uniform moisture content throughout the CLT or glulam in both the initial and final stages, that is, the influence of moisture gradient was ignored. This research investigated the stress distribution of the STS in the linear elastic regime. The elastic material properties were determined from a series of tests conducted on the STS, CLT, and glulam.
2.1. Tensile Test of Self-Tapping Screws
The STS of two diameters, 8 mm and 13 mm, were tested under uniaxial tension. The average Young’s modulus, yield strength, ultimate tensile strength, strain at failure, and strain at ultimate tensile strength were determined from these tests. However, only the average Young’s modulus of the screws was used in the finite element (FE) analysis since that was the only property required for linear elastic analysis by the FE model, in addition to Poisson’s ratio. The other screw properties can be used in future research to encapsulate the behavior of the screws in the post-elastic regime.
The screw configurations shown in
Table 2 were tested. The thread diameter in
Table 2 is the outer thread diameter of the screw, and the root diameter is the diameter of the inner core of the screw. The number of samples tested for each screw configuration is also stated in the table. More samples were tested for screw type B, which produced a less consistent load-deformation graph. In regard to screw type B, all the screws supplied by the manufacturer were tested.
The complete tension test setup with a specimen fitted inside the test fixture is shown in
Figure 2. The elongation of the screw was recorded with an extensometer attached to the thread of the screw. The applied load was measured by the load cell of the machine head. The ASTM standard E8/E8M-22 was followed for conducting the tensile tests [
9].
The load-elongation curves were recorded at approximately three data points per second and converted to stress–strain curves. The load at each data point was divided by the initial cross-sectional area of the core, excluding the threads, of the screw to calculate the stress. The change in length at each data point was divided by the gauge length over which the elongation was measured to determine the strain. Young’s modulus was determined by finding the slope of the fitted line of the initial linear portion of the stress–strain curve according to ASTM E111-17 [
10].
2.2. Swelling Test of CLT and Glulam
The swelling behavior of the CLT and glulam products mentioned in
Table 1 were investigated. The swelling coefficient of the individual laminates of the CLT and glulam was determined from the swelling strain versus moisture content change response. These swelling coefficient values were used as finite element model input for the different layers of the CLT and glulam.
Glulam of two different sizes from the same manufacturer and CLT made from 2 × 4 laminates (160 × 170 CLT) and 2 × 6 laminates (260 × 270 CLT) from two different manufacturers were tested. The two sizes of glulam and the two types of CLT used are shown in
Figure 3. According to the technical specifications of the CLT manufacturer, the longitudinal (major) and the transverse (minor) layers of CLT were made from lumber of different grades. Thus, the laminates of the longitudinal and transverse layers might have come from different sources, and the swelling properties of the longitudinal and the transverse layers of CLT were determined separately. Both sizes of glulam used in the test program were of the same grade and from the same manufacturer. Furthermore, the glulam was of compression grade, which means all the laminates were of the same grade. Thus, all the layers of both sizes of glulam were considered to have the same swelling properties.
Small-size samples of approximate dimensions of 80 (longitudinal) mm × 35 (radial) mm × 35 (tangential) mm were cut from the different layers of CLT and glulam. It was ensured that the samples had no glue on any face. Three sample groups were prepared with these small-sized samples to investigate the dimensional changes with moisture content change. The number and type of specimens in each sample group are summarized in
Table 3.
In two stages, each sample group was conditioned under constant relative humidity and temperature conditions. The conditioning time for each stage was two weeks. The samples were kept in a conditioning chamber in the first stage with 65 ± 2% relative humidity and a temperature of 20 °C. In the second stage, the samples were kept in another conditioning chamber. The three sample groups were kept in three different conditioning chambers in the second stage, as shown in
Table 4. The first conditioning stage was adopted to achieve an equilibrium moisture content (EMC) of 12% for all specimens. The second conditioning stage aimed to achieve EMCs of 6%, 16%, and 21% (
Table 4). All the samples reached a constant weight at the end of the two-week conditioning process, indicating uniform moisture content distribution inside the samples. After the two-stage conditioning, the samples were oven dried at 105 ± 1 °C for two days to achieve an oven-dry condition. The sample preparation, conditioning, and oven-drying process for the swelling tests are summarized in the flow chart shown in
Figure 4.
A total of nine length measurements from each sample, three along each orthotropic direction, were taken (
Figure 5). Each sample’s length and weight measurements were taken at the end of the second-stage conditioning and after oven drying. A digital balance with a precision of 0.01 g was used to measure sample weight, and a digital calliper with a precision of 0.01 mm was used to measure sample dimensions. The length measurements were later used to determine the swelling strains according to Equation (1). The actual moisture content of each sample was determined using Equation (2).
The swelling coefficient can be determined by determining the slope of the swelling strain versus moisture content change graph. For this purpose, the strain values along the three orthotropic directions were recorded under different known moisture content changes. The strain value and the moisture content change of a sample can be determined using Equations (1) and (2) [
6]:
where
and
are the oven-dry length and weight of the sample, respectively. Where
and
are the length and weight at the end of the second conditioning stage of the sample,
is the generated swelling strain, and
is the moisture content.
2.3. Withdrawal Test of Self-Tapping Screws in CLT and Glulam
Withdrawal tests were conducted on the identical specimens modelled in ABAQUS, as shown in
Figure 1. The STS of the two diameters, 8 mm and 13 mm, were inserted centrically in the CLT and glulam products at a 10 d (d is the outer nominal diameter of the screw) penetration length perpendicular to the face of the specimen. The specimens were conditioned in two stages. The two-stage conditioning was performed chronologically: to achieve the initial target equilibrium moisture content (EMC) before—screw installation—conditioning to reach the final target EMC. The two-stage conditioning process was adopted to simulate the condition that the moisture content of timber members might change after screw installation in practical settings. After achieving the final target EMC, the specimens were tested in displacement control under pull–push loading conditions. The five conditioning settings adopted for the withdrawal test specimens are shown in
Table 5. All the wood products and self-tapping screw combinations in the leftmost column of
Table 5 were conditioned under the five conditioning settings.
The test setup with a trial sample used for the withdrawal test is exhibited in
Figure 6. The withdrawal displacement of the screw from the top wood surface was measured with two displacement (linear variable differential transformer (LVDT)) transducers. The load-displacement curve for each specimen was recorded, from which the withdrawal strength and stiffness were determined. The load-displacement curves and withdrawal test data from the withdrawal tests were used in the finite element model as input parameters.
The withdrawal tests were performed to reach the maximum load within 90 ± 30 s according to the standard BS EN 1382-2016 [
11]. The withdrawal strength of each screw was calculated using the following equation [
12]:
Here, is the maximum applied load as measured by the machine head in N, is the outer thread diameter of the screw in mm, is the effective penetration length of the screw inside the specimen in millimeters. The effective penetration length of the screw excludes the length of the tip of the screw, which is not fully effective in imparting withdrawal resistance. The effective penetration length was determined according to the screw manufacturer’s guide.
The withdrawal displacement (
) of the screw is calculated using Equations (4) and (5) [
12]. In Equation (4), the elongation of the free part of the screw is subtracted from the transducer measurements to get the actual value of the withdrawal displacement of the screw inside the wood:
where
are the displacements recorded by the displacement transducers,
is the length of screw protrusion outside the CLT or glulam in millimeters,
is Young’s modulus of the material of the screw in MPa,
is the applied load at each data point in N,
defined in Equation (5) is the tensile stress in the screw in MP, and
is the inner core diameter of the screw in millimeters. The inner core diameter of the screw has been used here based on the premise that the screw core provides the axial rigidity of the protruded part of the screw. The effective length, based on the screw manufacturers’ guide, and the length of screw protrusion for the different screws used in the test program are mentioned in
Table 6.
The applied force and the corresponding withdrawal displacement calculated using Equation (4) were used to plot the load-displacement curve for each specimen. From the load-displacement response, the withdrawal stiffness was calculated according to Equation (6):
Here, is the slope of the linear fit-line between 10–40% of the maximum load of the load-displacement response, and the other terms are as explained before.
2.4. Numerical Modelling Technique
The numerical modelling technique adopted here was inspired by the work of Avez et al. [
13], Bedon et al. [
14], and Feldt and Thelin [
15]. The screw–wood composite model was created in ABAQUS/CAE [
7] and consisted of three parts: steel screw core; wood member; and soft layer. The screw core represents the core of the self-tapping screw, excluding the screw threads, the wood member represents the CLT or glulam, and the soft layer is representative of the screw thread and wood fibre interaction zone.
A 3D (dimensional) model is a practical choice for describing the orthotropic material properties of wood. However, the computational time required for numerical simulations with a 3D model is quite long. A 2D axisymmetric model significantly reduces the simulation time. The steel material of the screw is isotropic, and both 2D and 3D models can describe it. It was shown by Feldt and Thelin [
15] that the difference in the predicted pull-out capacity and stiffness of glued-in rods embedded in wood members using a 3D and a 2D axisymmetric model was very small. Thus, the 2D axisymmetric modelling technique was adopted to model the self-tapping screws inserted into CLT and glulam.
The 3D system of the self-tapping screw inserted centrically into CLT/glulam was reduced to an axisymmetric model, as shown in
Figure 7. The radius of the axisymmetric model is defined by the minimum of the (edge distance + d/2, where d is the outer thread diameter of the screw) and (end distance + d/2) of the screw inside the CLT/glulam. In ABAQUS/CAE, an axisymmetric model was generated by revolving a 2D plane about a symmetry axis and is described by a cylindrical coordinate system, as illustrated in
Figure 8. In
Figure 8, the symmetry axis lies along the longitudinal center line of the screw, which implies that the screw is placed centrically with the wood grain direction running along the cylinder’s circumferential direction.
The thermal analysis module in ABAQUS/CAE is analogous to the moisture-swelling process in wood. Thus, thermal analysis using the ABAQUS standard solver was carried out to simulate the moisture-swelling process in CLT and glulam. In the thermal analysis, the temperature is analogous to the wood’s moisture content, and the coefficient of thermal expansion is analogous to the wood’s swelling coefficient. The uniform moisture content in the wood member was specified as a predefined constant-temperature field. For example, the whole wood member was assigned the 12% moisture content condition with a constant predefined temperature of 12 (unitless). The wood moisture swelling coefficient along the three orthotropic directions was defined as the orthotropic coefficient of thermal expansion values in ABAQUS/CAE.
For simulating the screw pull-out behavior under moisture content variation, an axial load was applied to the top surface of the screw core in the finite element model under (1) displacement control and (2) force control, with proper support and moisture content, that is, in terms of temperature and boundary conditions. The displacement-controlled axial load was applied by specifying a displacement boundary condition. The force-controlled axial load was applied by specifying a concentrated force acting on top of the screw core.
The screw core and the wood were modelled as linear elastic materials, and the soft layer was assigned the same material properties as the wood member [
13]. The screw core was assigned isotropic material properties, whereas the wood was assigned orthotropic material properties. Local material orientation was assigned to the wood member, wherein the angular value was set per the average angle between the tangent to the annual rings and the horizontal direction of the CLT/glulam laminate’s end grain. The CAX4 elements of ABAQUS/CAE were used in the finite element model.
The screw core and the soft layer were rigidly connected with the “tie constraint” in ABAQUS/CAE, as the soft layer represents the integral threaded part of the screw embedded in the wood. A surface-based cohesive contact interaction was used to interconnect the external surface of the soft layer and the surrounding wood. In simpler terms, the soft layer was tied to the screw core on the inner side and cohesively bonded to the surrounding wood on the outer side, encapsulating the wood-screw thread interaction (
Figure 8, right). The cohesive contact in ABAQUS/CAE utilizes the cohesive zone modelling (CZM) approach based on nonlinear fracture mechanics. The bottom end of the screw was modelled as a free edge, as it has a negligible effect on the stress distribution of the screw during axial loading [
15]. The CZM approach is highly mesh-dependent, and a smaller element size is preferable. Mesh sizes of 0.5 mm for the 8 mm screw and 1 mm for the 13 mm screw were used for the screw core and the soft layer. For the CLT/glulam, a mesh size of 2 mm was used for all models. Both a free and structured mesh technique was used, and both techniques produced similar results. Enlarged pictures of the mesh of the models are shown in
Figure 9.
The CZM approach can adequately describe the pull-out behavior of the screw during axial loading [
13]. The cohesive contact interaction in ABAQUS/CAE requires three input parameters: an elastic behavior defined by the stiffness values, a damage initiation criterion, and a damage evolution model. The stiffness values along three directions were the normal direction (K
nn), which is perpendicular to the screw longitudinal axis; and the two transverse (shear) directions (K
ss and K
tt), wherein one was parallel to the screw longitudinal axis and one was parallel to the tangent to the cylindrical screw surface (
Figure 10, right). The stiffness of the normal direction is less critical in this study as the axial loading is of primary interest here. The stiffness values along the two shear directions were assumed to be equal. The two shear directions correspond to the direction parallel to the screw axis and the direction tangent to the screw diameter. Since the 2D axisymmetric modelling technique is adopted here, the shear direction parallel to the screw axis affects the numerical solution. Assuming the same value of stiffness along the other shear direction tangent to the screw diameter has no effect on the numerical solution,, according to the traction separation law, the stiffness values relate the tractions (t
n, t
s, t
t) in the three directions to the separation (
) in the respective directions (
Figure 10, left).
The quadratic traction damage initiation criterion was used to determine the failure of the screw–wood interaction zone. The criterion is given by Equation (7):
Here,
is the normal tension traction;
and
are the tractions in the two shear directions; and
,
and
are the maximum tractions in the three directions when the separation is either purely normal to the screw interface or acts purely in the shear directions. The symbol ⟨ ⟩ signifies that a purely compressive displacement or a purely compressive stress state does not initiate damage [
7].
Once the failure criterion is satisfied, the damage evolution model gives the stresses in the three directions. A linear energy-based softening model without considering mode-mixing was used as the damage evolution model. The total fracture energy per unit area (
Gfn,
Gfs,
Gft) in each mode was equal, and only one value of the total fracture energy was defined. The fracture energy per unit area was calculated as:
The pressure–overclosure relationship type was set to “hard” contact, and the default constraint enforcement method was used to describe the normal behavior for the cohesive contact in ABAQUS/CAE. For the tangential behavior of cohesive contact, the “penalty friction” formulation with a friction coefficient of 0.2 was used [
16]. Finally, the small sliding formulation was used in ABAQUS/CAE to define the cohesive contact interaction for better convergence.