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Abstract

A sequentially coupled thermo-mechanical finite element model is used to simulate the friction stir welding process. Fracture mechanical models for the middle tension specimen and the eccentrically loaded single-edge crack tension specimen are established. Utilizing the residual stress intensity factor obtained by the fracture mechanical models, the crack-closure model and superposition method are adopted to predict the fatigue crack growth rates of the two specimens. The results indicate that the effect of the residual stress on the fatigue crack growth rate becomes obvious as the stress ratio decreases. Considering the residual stress, the fatigue life of the welded plate exhibits a dramatic decrease for the middle tension specimen, but a remarkable increase for the eccentrically loaded single-edge crack tension specimen. The fatigue life of the middle tension specimen is almost insensitive to the rotational speed, but that of the eccentrically loaded single-edge crack tension specimen increases with the increase in the rotational speed.

Keywords

Friction stir welding fatigue crack growth rate fatigue life residual stress rotational speed

Introduction

Friction stir welding (FSW) technology has a wide application in aerospace, automobile and shipping industries due to its excellent properties, such as high strength, low distortion and reduced occurrence of defects.^1–3 Compared with the conventional riveting technique, the cost and weight of the integral structures can be reduced.⁴ However, it is notable that the weld-induced residual stress may have an obvious effect on the damage tolerance⁵ and the service life.^6,7 Hence, a lot of work has been done to study the influence of the residual stress on the fatigue crack growth rate (FCGR) of the welded structures.^8–14

Bussu and Irving⁸ studied the surface crack tension specimen and the compact tension specimen using experimental method. The results indicate that the FCGR in the welded plate strongly depends on the location and orientation with respect to the weld line, and the crack growth behavior in the weld zone is generally dominated by the residual stress. Ma et al.^9,10 studied the effect of the plate size on the FCGR in friction stir welded specimen by both experimental and numerical methods. The superposition method and the crack-closure model are usually adopted to predict the FCGR in weld-induced residual stress field.¹¹ For these two methods, the calculation of residual stress intensity factor ( $K_{res}$ ) is the most important part.¹² The weight function method (WFM) or the finite element method (FEM) can be used to calculate $K_{res}$ .¹² Al-Mukhtar¹³ determined the residual stress and $K_{res}$ by WFM to assess the FCGR of the welded steel joints. The results reveal that the transverse residual stress has a significant effect on the FCGR in the thickness direction. Servetti and Zhang¹⁴ investigated the FCGR in weld-induced residual stress field using different empirical equations, namely, the Walker equation, the Harter T-method and the NASGRO equation. It is indicated that the results obtained by the Harter T-method and the NASGRO equation are in good agreement with the experimental data.

Although scholars have achieved numerous useful conclusions, not much work has been carried out to study the influence of the residual stress on the fatigue life of the friction stir welded AA 2024-T3 joint and the effect of the rotational speed on the fatigue life of the welded plate. In this work, a sequentially coupled thermo-mechanical model is used for FSW simulation with different rotational speeds. The obtained residual stress is rebalanced in the fracture mechanical model to calculate $K_{res}$ with different crack lengths. Then, the FCGR of the welded plate is predicted. By coupling of the FCGR, the fatigue life of the welded plate can be obtained.

Model descriptions

Sequentially coupled thermo-mechanical model

The governing equation of the transient heat transfer analysis can be written as^15–17

ρ c \frac{\partial T}{\partial t} = div \cdot (k \cdot divT) + Q_{int}

(1)

where $ρ$ is the material density, c is the specific heat capacity, $T$ is the temperature, $t$ is the time, $k$ is the thermal conductivity coefficient and $Q_{int}$ is the volumetric heat flux.

The frictional heat between the welding tool and the plates is considered as a moving surface heat source and a moving body heat source¹⁸

\begin{matrix} q_{s} (x, y, z) = \frac{3 Q_{s} \sqrt{{(x - x_{0} - vt)}^{2} + y^{2}}}{2 π (R^{3} - R_{1}^{3})} \\ (R_{1} \leq \sqrt{{(x - x_{0} - vt)}^{2} + y^{2}} \leq R, on Γ_{2}) \end{matrix}

(2)

q_{p} = \frac{Q_{p}}{π R_{1}^{2} H} (\sqrt{{(x - x_{0} - vt)}^{2} + y^{2}} \leq R_{1}, in Ω)

(3)

where $Q_{s}$ and $Q_{p}$ are the heat power generated by the shoulder and the stirring pin, respectively; R₁ and H are the radius and the height of the stirring pin, respectively (R₁ = 3.175 mm and H = 6 mm); $R$ is the radius of the shoulder (R = 9.5 mm); x₀ is the starting position of FSW process (x₀ = 10 mm); v is the welding speed; q_s is the given heat flux density on Γ₂; and q_p is the volumetric heat flux. The bottom surface is considered as convective boundary condition. The coefficient of the surface film conductance is 1000 W/(m² °C).¹⁹ The coefficient of surface film conductance between the welding plate and the air is 30 W/(m² °C). The ambient temperature is 20 °C.

In the thermo-mechanical analysis, the fixtures are treated as rigid constraints in the welding and the subsequent cooling processes, as shown in Figure 1. When the plate is cooled down to the ambient temperature, the rigid constraints are released. Then, point A is constrained in all the three directions and point B is fixed in the transverse and thickness directions.

Figure 1.

Meshing condition and constraints for the thermo-mechanical analysis.

The plate size is 200 × 80 × 6 mm, as illustrated in Figure 1. The transverse speed is 2 mm/s. The rotating speeds are 300, 650 and 1000 r/min, respectively. The eight-node linear brick element is used for the heat transfer analysis and the subsequent thermo-mechanical analysis. The finite element model consists of 286,179 nodes and 270,000 elements. The smallest element size is 0.5 × 0.5 × 0.5 mm.

The Johnson–cook (J-C) material model²⁰ is adopted to describe the mechanical behavior of Al 2024-T351. The J-C model incorporates strain rate, temperature and strain hardening effects,^21–23 which can be written as

σ_{s} = (A + B ε_{p}^{n}) (1 + C \ln (\frac{{\overset{\cdot}{ε}}_{p}}{{\overset{\cdot}{ε}}_{0}})) (1 - {(T^{*})}^{m})

(4)

where A, B, C, n and m are material constants; $σ_{s}$ is the yield stress at nonzero strain rate; $ε_{p}$ , ${\overset{\cdot}{ε}}_{p}$ and ${\overset{\cdot}{ε}}_{0}$ are the equivalent plastic strain, the strain rate and the reference strain rate, respectively; and $T^{*}$ is the normalized temperature defined as

T^{*} = {\begin{matrix} 0 & T < T_{ref} \\ (T - T_{ref}) / (T_{melt} - T_{ref}) T_{ref} < T < T_{melt} \\ 1 & T > T_{melt} \end{matrix}

(5)

where $T_{ref}$ is the reference temperature and $T_{melt}$ is the melting temperature. Material properties and parameters of the J-C model²⁴ are presented in Table 1.

Table 1.

Material properties and parameters used for Al 2024-T351.²⁴

Thermal conductivity (W/(m °C))	Specific heat (J/(kg °C))	Density (kg/m³)	Young’s modulus (GPa)	Poisson’s ratio	A (MPa)	B (MPa)	C	n	m
121	875	2770	73	0.34	369	684	0.0083	0.73	1.7

Fracture mechanical model

In this work, two-dimensional (2D) fracture mechanical models for the middle tension (M(T)) specimen and the eccentrically loaded single-edge crack tension (ESE(T)) specimen are established based on linear elastic fracture mechanics, as shown in Figure 2. Due to symmetry, only the half parts of the M(T) and ESE(T) specimens are modeled. The residual stress obtained from the sequentially coupled thermo-mechanical model is incorporated into the fracture mechanical model using the ABAQUS subroutine called SIGINI. The $K_{res}$ can be calculated by rebalancing of the residual stress in the fracture mechanical model. The collapsed element²⁵ is used to control the singularity at the crack tip, as shown in Figure 3. One side of the eight-node isoparametric element (see Figure 3(a)) is collapsed, so that all three nodes 2, 3 and 6 have the same geometric location (see Figure 3(b)). Then, by moving the mid-side nodes 5 and 7 to the quarter positions, the square root singularity can be exactly simulated. The J-integral method introduced by Rice²⁶ is employed to calculate the stress intensity factor. The J-integral is theoretically path independent. However, the first layer is not appropriate for the calculation of stress intensity factor because of numerical singularity at the crack tip. Thus, the J-integral is calculated from the second layer or even further from the crack tip meshed with eight-node isoparametric element, as shown in Figure 3(c). The J-integral and the stress intensity factors can be written as

J = \frac{K_{I}^{2} + K_{II}^{2}}{\bar{E}}

(6)

where $K_{I}$ and $K_{II}$ are the stress intensity factors for modes I and II conditions, respectively, $\bar{E} = E$ for plane stress and $\bar{E} = E / (1 - ν^{2})$ for plane strain. For mixed-mode condition, a simple application of J-integral cannot provide sufficient information for the separation of $K_{I}$ and $K_{II}$ . Thus, the auxiliary stress, strain and displacement fields need to be introduced into the fracture mechanical model. In this work, only the longitudinal residual stress obtained from the thermo-mechanical analysis is considered. The $K_{res}$ can be obtained by

K_{res} = K_{I}^{(1)} = \frac{\bar{E}}{2} \int_{Γ} [σ_{ik}^{(1)} ε_{ik}^{(2)} δ_{1 j} - σ_{ij}^{(2)} \frac{\partial u_{i}^{(1)}}{\partial x_{1}} - σ_{ij}^{(1)} \frac{\partial u_{i}^{(2)}}{\partial x_{1}}] n_{j} d Γ

(7)

Figure 2.

Fracture mechanical model for the (a) M(T) and (b) ESE(T) specimen.

Figure 3.

Element condition at the crack tip: (a) isoparametric element, (b) collapsed element and (c) element around crack tip.

Here, two states are considered: State 1 ( $σ_{ij}^{(1)}, ε_{ij}^{(1)}, u_{ij}^{(1)}$ ) corresponds to the present state induced by the balance of the residual stress in the fracture mechanical model. State 2 ( $σ_{ij}^{(2)}, ε_{ij}^{(2)}, u_{ij}^{(2)}$ ) is an auxiliary state, and detailed information can be found in the ABAQUS theory manual.²⁷

The applied load range is 45 MPa for M(T) specimen and 8 kN for ESE(T) specimen performed at R = 0.1, 0.3 and 0.5.

FCGR prediction

The superposition approach and the crack-closure model²⁸ are adopted to predict the FCGR of the M(T) specimen and the ESE(T) specimen, respectively. The flowchart of the two methods is given in Figure 4. As $K_{res}$ , $K_{app, max}$ and $K_{app, min}$ are obtained using the fracture mechanical model, the applied stress intensity factor range ( $Δ K_{app}$ ) and the effective stress intensity factor ratio ( $R_{eff}$ ) can be calculated by

\begin{matrix} Δ K_{app} = (K_{app, max} + K_{res}) - (K_{app, min} + K_{res}) \\ = K_{app, max} - K_{app, min} \end{matrix}

(8)

and

R_{eff} = \frac{K_{app, min} + K_{res}}{K_{app, max} + K_{res}}

(9)

Figure 4.

Flowchart of (a) crack-closure model and (b) superposition approach.

The stress ratio can be written as

R = \frac{K_{app, min}}{K_{app, max}}

(10)

The effect of residual stress on $R_{eff}$ becomes obvious when the difference between $R_{eff}$ and R is increased.

For superposition approach, the NASGRO equation is written as¹⁴

\frac{da}{dN} = C ″ {((\frac{1 - f}{1 - R_{eff}}) Δ K_{app})}^{n ″} \frac{{(1 - \frac{Δ K_{th}}{Δ K})}^{p}}{{(1 - \frac{K_{Kapp, max} + K_{res}}{K_{crit}})}^{q}}

(11)

where $C ″$ , $n ″$ , f, p and q are material parameters; $Δ K_{th}$ and $K_{crit}$ are the threshold stress intensity factor and the critical stress intensity factor, respectively. The parameters used in NASGRO equation¹⁴ are listed in Table 2.

Table 2.

Parameters used in superposition approach and crack-closure model.^14,29

$C ″$	$n ″$	p	q	$C'$	$n'$
1.71 × 10⁻¹⁰	3.353	0.5	1	1.0327 × 10⁻¹⁴	4.1925

For crack-closure model, the equations introduced by Newman³⁰ can be used to calculate the ratio of the opening stress ( $S_{o}$ ) and the maximum applied stress ( $S_{max}$ ) as follows

\frac{S_{0}}{S_{max}} = {\begin{matrix} A_{0} + A_{1} R + A_{2} R^{2} + A_{3} R^{3} & R \geq 0 \\ A_{0} + A_{1} R & R < 0 \end{matrix}

(12)

The coefficients used in equation (12) can be written as³⁰

A_{0} = (0.825 - 0.34 α + 0.05 α^{2}) {[\cos (π S_{max} / 2 σ_{0})]}^{1 / α}

(13)

A_{1} = (0.415 - 0.071 α) S_{max} / σ_{0}

(14)

A_{2} = 1 - A_{0} - A_{1} - A_{3}

(15)

A_{3} = 2 A_{0} + A_{1} - 1

(16)

The effective stress intensity factor range ( $Δ K_{eff}$ ) is given by

Δ K_{eff} = \frac{1 - \frac{S_{0}}{S_{max}}}{1 - R} Δ K_{app}

(17)

$R_{eff}$ is used in equations (12) and (17) instead of R considering the residual stress.¹⁰

The FCGR can be calculated by

\frac{da}{dN} = C' {(Δ K_{eff})}^{n'}

(18)

where $C'$ and $n'$ are the material constants,²⁹ which are given in Table 2. Then, the fatigue life can be obtained with integral of the FCGR over the crack length.

Model verification

Experimental data from the literature^4,14,31 are employed to verify the model used in this work. The M(T) specimen is illustrated in Figure 5. Longitudinal residual stress is rebalanced in the fracture mechanical model in order to calculate $K_{res}$ . The rebalanced residual stresses with crack propagation are compared with the experimental data,⁴ as shown in Figure 6. It can be observed that the residual stresses from the FEM are higher than the experimental data at the crack tip due to the singularity. However, the predicted results agree well with the experimental data⁴ away from the crack tip. The singularity at the crack tip does not affect the calculation of the $K_{res}$ as the integral domain is out of the singular domain (see Figure 3). The $K_{res}$ calculated by J-integral agrees well with the virtual crack-closure technique (VCCT) result,¹⁴ as shown in Figure 7.

Figure 5.

Sketch of the middle crack specimen.

Figure 6.

Residual stress redistribution at different crack lengths.

Figure 7.

Comparison of the predicted J-integral result with the VCCT result.

The FCGR is obtained using the superposition method. The validation of the predicted FCGR with the experimental data³¹ is shown in Figure 8. Moreover, the fatigue life can be obtained with integral of the FCGR, as illustrated in Figure 9. The predicted results agree well with the experimental data.³¹

Figure 8.

FCGR validation with the experimental data.

Figure 9.

Fatigue life validation with the experimental data.

Results and discussions

Weld-induced residual stress

In the published literature,^18,32,33 the predicted longitudinal residual stresses in the weld zone are slightly higher than the experimental data. The reason is that the material properties in the weld zone are set to be identical to the base material. Actually, according to the experiments,^34–38 it can be found that the yield strength of the material in the weld zone can be reduced to 38%–75% compared with the base material. By trial-and-error tests, the predicted results agree well with the experimental data³⁹ when the yield strength of the material in the weld zone is reduced to 56%, as shown in Figure 10. Hence, in this work, 56% yield strength of base material is chosen for the yield strength of the material in the weld zone.

Figure 10.

Comparison of the predicted residual stress to the experimental data.

From Figure 11, it can be seen that the maximum Mises stress is only 131.8 MPa at 300 r/min, which is far less than the yield strength of the base material. The longitudinal residual stress in the transverse section is selected for the calculation of the $K_{res}$ , as shown in Figure 12. Tensile stress is observed in the weld zone. Away from the weld zone, the residual stress decreases and finally compressive stress is observed. After the rebalance of the residual stress in the fracture mechanical model, stress concentration is observed at the crack tip, as shown in Figures 13 and 14.

Figure 11.

Residual stress distribution of FSW, 300 r/min.

Figure 12.

Longitudinal residual stress profile of FSW.

Figure 13.

Balance of residual stress for M(T) specimen, 300 r/min.

Figure 14.

Balance of residual stress for ESE(T) specimen, 300 r/min.

Residual stress intensity factor at 300 r/min

The stress intensity factor from the applied load can be calculated using the empirical equation. For M(T) specimen⁴⁰

K = σ \sqrt{π a} \sqrt{\sec \frac{π a}{W}}

(19)

where W is the width of the specimen. For ESE(T) specimen⁴¹

Δ K = (\frac{Δ P}{(B \sqrt{W})}) F

(20)

and

F = β^{1 / 2} (1.4 - β) {(1 - β)}^{- 3 / 2} G

(21)

where

\begin{matrix} G = & 3.97 - 10.88 β + 26.25 β^{2} - 38.9 β^{3} \\ + 30.15 β^{4} - 9.27 β^{5} \end{matrix}

(22)

for 0 <β < 1, $β = a / W$ .

As shown in Figures 15 and 16, the predicted results from the fracture mechanical models agree well with the results calculated by the empirical equations, which further indicate the validity of the fracture mechanical models used in this work.

Figure 15.

Comparison of the FEM result with the empirical result, M(T) specimen.

Figure 16.

Comparison of the FEM result with the empirical result, ESE(T) specimen.

The stress distributions around the crack tip after the rebalance of the residual stress are given in Figures 17 and 18. For the M(T) specimen, the initial crack locates in the tensile residual stress field. The stress around the crack tip is always tensile stress, which increases as the crack propagates to the edge of the weld zone. This is the reason that the $K_{res}$ increases as the crack propagates to the weld edge, as shown in Figure 19. Moreover, it is observed that the maximum $K_{res}$ of the M(T) specimen locates at positions 1 and 2 near the edge of the weld zone. When the crack propagates from the tensile residual stress field into the compressive residual stress field, the tensile stress around the crack is reduced. Hence, the $K_{res}$ is decreased, and the trend of K_res is similar to that of the residual stress.

Figure 17.

Stress distribution around the crack tip at different crack lengths, M(T).

Figure 18.

Stress distribution around the crack tip at different crack lengths, ESE(T).

Figure 19.

K_res and the residual stress profiles, 300 r/min.

For ESE(T) specimen, the initial crack locates in the compressive residual stress field, and compressive stress can be observed around the crack tip after the rebalance of the residual stress, as shown in Figure 18. This is the reason that the $K_{res}$ is negative. The compressive stress is increased with the crack propagation from 5 to 25 mm. Hence, the $K_{res}$ is decreased and the minimum $K_{res}$ is observed at position 3, as shown in Figure 19. The compressive stress is decreased when the crack propagates from 25 to 45 mm. Thus, the $K_{res}$ can be increased, and the maximum $K_{res}$ is observed at position 4. When the crack propagates from 52 to 66 mm, tensile stress around the crack tip is decreased so that the $K_{res}$ is positive and decreased with the crack propagation. The K_res curve is obviously different to the residual stress curve for ESE(T) specimen. The residual stress intensity factor value starts negative and moves into positive for ESE(T) specimen that is consistent with the previous work.¹⁰

Effect of residual stress on the fatigue life of the welded specimen at 300 r/min

The residual stress has a significant effect on the $R_{eff}$ , as shown in Figures 20 and 21. For M(T) specimen, K_res is positive. Considering equation (9), the $R_{eff}$ can be increased. The maximum differences between the R and the $R_{eff}$ can be found when the $R_{eff}$ reaches its maximum value, as illustrated in Figure 20. The maximum values of the $R_{eff}$ are 0.6, 0.65 and 0.71 at R = 0.1, 0.3 and 0.5, respectively. For ESE(T) specimen, the K_res is negative when the crack propagates to the weld zone. Hence, the $R_{eff}$ can be decreased considering equation (9). The maximum differences between the R and the $R_{eff}$ can be found when the $R_{eff}$ reaches its minimum value, as shown in Figure 21. The $R_{eff}$ are −2.4, −0.63 and 0.16 at R = 0.1, 0.3 and 0.5, respectively. It can be concluded that the influence of the residual stress on the $R_{eff}$ decreases with the increase in the stress ratio.

Figure 20.

Effect of residual stress on R_eff, M(T) specimen.

Figure 21.

Effect of residual stress on R_eff, ESE(T) specimen.

The FCGRs at R = 0.1, 0.3 and 0.5 are given in Figures 22 and 23. When the initial location of the crack is in the tensile residual stress field, the FCGR can be increased, as shown in Figure 22. The FCGR of the welded plate can reach 2.4 times higher than the FCGR of the base material at a = 11 mm, R = 0.3. After the rebalance of the residual stress in the fracture model, the stress around the crack tip is tensile stress. Tensile stress can increase the FCGR.^8,42 Hence, the FCGR of the welded plate can be increased, even though the crack propagates from the tensile residual stress field into the compressive residual stress field for M(T) specimen. From Figure 23, it can be found that the FCGR can be obviously decreased when the initial location of the crack is in the compressive residual stress field. The stress around the crack tip is compressive stress as the crack length is less than 45 mm. Compressive stress can decrease the FCGR.^8,42 Therefore, the FCGR of the welded plate can be decreased, even though the crack propagates from the compressive residual stress field into the tensile residual stress field. When the crack length is more than 52 mm, the stress around the crack tip is tensile stress, and the FCGR of the welded plate can be increased compared with that of the base material, as shown in Figure 23. At a = 23 mm and R = 0.3, the FCGR in the welded plate can be only 5% of the FCGR in the base material. From Figures 22 and 23, it can be found that the effect of residual stress on the FCGR decreases with the increase in the stress ratio.

Figure 22.

Predicted FCGR at different stress ratios, M(T) specimen.

Figure 23.

Predicted FCGR at different stress ratios, ESE(T) specimen.

The function $H (a)$ is defined as

\begin{matrix} H (a) = \\ {\begin{matrix} 1 (if the FCG of the welded plate is increased) \\ - 1 (if the FCG of the welded plate is decreased) \end{matrix} \end{matrix}

(23)

From Figure 24, it can be seen that the residual stress intensity factor can directly reflect the influence of residual stress on the FCGR of the welded plate, and the FCGR can be increased by positive residual stress intensity factor and decreased by negative residual stress intensity factor.

Figure 24.

Residual stress intensity factor and H(a) distribution, ESE(T).

The fatigue life can be obviously decreased for M(T) specimen, as shown in Figure 25. As a = 1 mm, the fatigue life of the welded plate can be decreased by 51% compared with the base material. However, the fatigue life can be increased for ESE(T) specimen, as shown in Figure 26. As a = 1 mm, the fatigue life of the welded plate can reach 8.8 times higher than the fatigue life of the base material.

Figure 25.

Fatigue life of the M(T) specimen with different crack lengths, R = 0.3.

Figure 26.

Fatigue life of the ESE(T) specimen with different crack lengths, R = 0.3.

Effect of the rotational speed on the fatigue life of the welded plate

The maximum residual stress is increased by increasing the rotational speed, as shown in Figure 27. This phenomenon has been observed in the published literature.⁴³ The tensile residual stress field becomes wider with the increase in the rotational speed.

Figure 27.

Longitudinal residual stress profiles at different rotational speeds.

The tensile stress around the crack tip can be decreased by increasing the rotational speed when the crack length is 7 mm, as shown in Figure 28. Hence, the FCGR of the welded plate can be decreased by increasing the rotational speed. When the crack is 1 mm, the fatigue lives at 650 and 1000 r/min are increased by 2.1% and 3.9%, respectively, compared with the fatigue life at 300 r/min, 418,414 cycles. The influence of the rotational speed on the fatigue life of the M(T) specimen is very small, as shown in Figure 29. When the crack length is 11 mm, the fatigue lives at 650 and 1000 r/min are decreased by 7.4% and 14.3%, respectively.

Figure 28.

Stress distribution around the crack tip with different rotational speeds, M(T).

Figure 29.

Influence of rotational speed on the fatigue life of M(T) specimen, R = 0.3.

After the rebalance of the residual stress in the fracture mechanical model, the compressive stress around the crack tip is increased with the increase in the rotational speed when the crack length is 5 mm, as shown in Figure 30. Thus, the FCGR is decreased considering the residual stress when the rotational speed is increased. The fatigue life of the welded plate can be increased by increasing the rotating speed, as shown in Figure 31. The fatigue lives at 300, 650 and 1000 r/min are 499,481, 963,425 and 2,355,755 cycles, respectively, at a = 15 mm.

Figure 30.

Stress distribution around the crack tip with different rotational speeds, ESE(T).

Figure 31.

Influence of rotational speed on the fatigue life of ESE(T) specimen, R = 0.3.

Conclusion

The following conclusions are drawn:

By comparing the experimental data, the proposed sequentially coupled thermo-mechanical model for FSW is validated.

The effect of the residual stress on the fatigue life of the welded plate depends on the initial crack location. For M(T) specimen, the initial crack locates in the tensile residual stress field and the stress around the crack tip is tensile after the rebalance of the residual stress in the fracture mechanical model so that the fatigue life can be decreased compared to the base material. For ESE(T) specimen, the initial crack locates in the compressive residual stress field and the stress around the crack tip is compressive so that the fatigue life can be increased.

The influence of the rotational speed on the fatigue life is more obvious for ESE(T) specimen than M(T) specimen. With the increase in the rotational speed, the compressive residual stress away from the weld zone increases. Hence, the fatigue life of the ESE(T) specimen can be increased when the rotational speed is increased.

The residual stress distribution is different to the residual stress intensity factor distribution for ESE(T) and is similar with the residual stress intensity factor distribution for M(T) specimen.

Footnotes

Appendix 1 Declaration of conflicting interests

The authors declare that there is no conflict of interest.

Funding

This work was supported by Program for New Century Excellent Talents in University, the Fundamental Research Funds for the Central Universities, the National Natural Science Foundation of China (nos 11172057 and 11232003), the National Key Basic Research Special Foundation of China (2011CB013401) and the National High Technology Research and Development Program of China (2012AA050901).

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Effect of residual stress of friction stir welding on the fatigue life of AA 2024-T351 joint

Abstract

Keywords

Introduction

Model descriptions

Sequentially coupled thermo-mechanical model

Fracture mechanical model

FCGR prediction

Model verification

Results and discussions

Weld-induced residual stress

Residual stress intensity factor at 300 r/min

Effect of residual stress on the fatigue life of the welded specimen at 300 r/min

Effect of the rotational speed on the fatigue life of the welded plate

Conclusion

Footnotes

Appendix 1

Declaration of conflicting interests

Funding

References