A Thermoelastic Stress Analysis General Model: Study of the Influence of Biaxial Residual Stress on Aluminium and Titanium
Abstract
:1. Introduction
2. Theory
- The applied mean stress , here considered proportional to for each pixel in a fixed test;
- the residual stress; and
- own weight of the structure.
3. Materials and Methods
3.1. Error Analysis in Stresses Evaluation if Residual Stresses Are Neglected
3.2. TSA Capability in Evaluating Residual Stresses: Statistical Analysis
- Signal amplitude calculation (Equation (13));
- Signal temporal reconstruction, assuming a sampling frequency of 200 Hz;
- Adding the gaussian noise according to the experimental value found with a cooled IR camera FLIR X6540sc, as described in the previous section; and
- Performing a Fast Fourier Transform to obtain the amplitude of the signal.
4. Results and Discussion
4.1. Effects of Biaxial Residual Stresses on TSA Signal
4.2. Error Analysis: Results
- The classical procedure presents the higher error;
- In the case of higher residual stress influence (γr = −2, θ = 90°), both the procedures give significant errors in stress amplitude evaluation, above 10%;
- The error increases as the stress amplitude increases for both the approaches. It is more significant for the Galietti et al. [17] approach in which the effect of the mean stress is considered; and
- The error always increases as the mean stress increases for the classic procedure while it decreases for the Galietti et al. [17] approach.
4.3. Capability in Evaluating Residual Stresses: Results
5. Conclusions
- The error in stress amplitude evaluation with TSA if the residual stresses are neglected depends on the modulus, direction and angle of the principal residual stresses with respect to the applied stresses. Significant errors (above 10%) can be made in stresses evaluation;
- This error depends also on the applied stresses (amplitude and mean) and on the considered material (thermo-physical and mechanical property); and
- In the same way, the capability of TSA in residual stresses evaluation depend on the considered material and on the modulus, direction and angle of the principal residual stresses with respect to the applied stresses.
Author Contributions
Funding
Conflicts of Interest
Nomenclature
dT | [K] | Infinitesimal temperature difference due to the thermoelastic effect |
T | [K] | Reference temperature |
[μm/m] | Vector of Infinitesimal strain variations | |
[μm/m] | Vector of strains in a point | |
[Pa] | Stiffness matrix | |
[K−1] | Vector of the linear thermal expansion coefficients | |
ρ | [kg/m3] | Density |
Cε | [J/kg·K] | Specific Heat at constant strain |
x, y, z | - | Reference system |
[Pa] | Vector of stress in a point | |
[Pa] | Vector of Infinitesimal stress variations | |
[Pa] | Amplitude stress vector | |
[Pa] | Total mean stress vector | |
[Pa] | Applied mean stress vector | |
[Pa] | Residual stress vector | |
1,2,3 | - | Principal system |
R | - | Rotation matrix |
θ | - | Angle between the residual stress principal system and the loading system |
a, b | [Pa−1], [Pa−2] | Thermoelastic parameters [16,17] |
c | [Pa−1] | Parameter depending on thermoelastic behaviour and residual stress |
γr | - | Ratio between the principal residual stress components |
γ | - | Ratio between the mean and amplitude of the load |
K | [Pa−1] | Thermoelastic constant [1] |
ε | - | Error affecting the stress amplitude measurement |
- | Error affecting the stress amplitude measurement using the classical technique | |
- | Error affecting the stress amplitude measurement using the method proposed by Galietti et al. [17] | |
β | - | Second type error |
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Material | α [K−1] | ρ [Kg/m3] | Cp [J/Kg·K] | Cε1 [J/Kg·K] | E [GPa] | υ | ∂E/∂T [MPa/K] | Rp0.2 [MPa] |
---|---|---|---|---|---|---|---|---|
AA6082 | 23.2 × 10−6 | 2.70 × 103 | 890 | 890 | 70 | 0.33 | −36 | 260 |
Ti6Al4V | 8.6 × 10−6 | 4.43 × 103 | 560 | 560 | 114 | 0.34 | −48 | 1100 |
Material | ∆σxx [MPa] | R | σmxx [MPa] | σr11 [MPa] | γr 1 | θ [°] |
---|---|---|---|---|---|---|
AA6082 | 60 | 0.1 | 73 | From −100 to 100 | From −2 to 1 | From 0 to 360 |
Ti6Al4V | 180 | 0.1 | 220 | From −100 to 100 | From −2 to 1 | from 0 to 360 |
Material | ∆σxx [MPa] | σmxx [MPa] | σr11 [MPa] | Residual Stresses System |
---|---|---|---|---|
AA6082 | 35, 70 | 0, 70, 140 | From 0 to 100 | γr = 1 and θ = 0 (low residual stresses effect) γr = −2 and θ = 90° (high residual stresses effect) |
Ti6Al4V | 100, 200 | 0, 200, 400 | From 0 to 100 | γr = 1 and θ = 0 (low residual stresses effect) γr = −2 and θ = 90° (high residual stresses effect) |
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Di Carolo, F.; De Finis, R.; Palumbo, D.; Galietti, U. A Thermoelastic Stress Analysis General Model: Study of the Influence of Biaxial Residual Stress on Aluminium and Titanium. Metals 2019, 9, 671. https://doi.org/10.3390/met9060671
Di Carolo F, De Finis R, Palumbo D, Galietti U. A Thermoelastic Stress Analysis General Model: Study of the Influence of Biaxial Residual Stress on Aluminium and Titanium. Metals. 2019; 9(6):671. https://doi.org/10.3390/met9060671
Chicago/Turabian StyleDi Carolo, Francesca, Rosa De Finis, Davide Palumbo, and Umberto Galietti. 2019. "A Thermoelastic Stress Analysis General Model: Study of the Influence of Biaxial Residual Stress on Aluminium and Titanium" Metals 9, no. 6: 671. https://doi.org/10.3390/met9060671