“…A continuum domain (Ω) bounded by boundary (Γ) is partitioned into boundary (Γt) with prescribed traction, traction free boundaries (Γs), and boundary (Γu) with prescribed displacement as shown in Figure 1. The equilibrium equations along with boundary conditions are given as (Kumar et al., 2016; Singh et al., 2017) where σ is the stress tensor, n is the unit normal vector, b represents the body force per unit volume, u is the displacement field vector, and t¯ represents the traction vector. Figure 1.Two-dimensional homogeneous body.…”
Section: Mathematical Formulationmentioning
confidence: 99%
“…Application of Gauss quadrature in enriched element subtriangularization technique is quite popular. While performing subtriangularization the number of Gauss points and their location changes in an element (Kumar et al., 2016). As per equation (7), the damage is calculated at the Gauss points and if the position and number of these Gauss points change with crack advancement, it will be cumbersome to evaluate the damage variable properly.…”
Section: Mathematical Formulationmentioning
confidence: 99%
“…Both local and nonlocal approaches are used. The iterative scheme for creep crack growth simulation is as follows (Hsu and Zhai, 1984; Kumar et al., 2016; Levy, 1981) For a given mesh and crack position, at time t=0, initialize damage variable ω=0and change in stress Δσ=0 at each Gauss point.Elasto-plastic analysis, Perform elasto-plastic analysis by assuming that at a material point, the state of stress at step i is known. So the known quantities are id,iε,iσ,iCe.Apply the incremental external force vector Δfext and calculate the total external force for the current load step (i+1) as Initialize the variables j-1i+1d,j-1i+1ε,…”
Section: Numerical Implementationmentioning
confidence: 99%
“…A theta projection model for creep behavior was established by Evans and Wilshire (1985). Further, Kumar et al. (2016) modified the theta projection method to improve the accuracy of modeling.…”
In the present work, elasto-plastic creep crack growth simulations are performed using continuum damage mechanics and extended finite element method. Liu–Murakami creep damage model and explicit time integration scheme are used to evaluate the creep strain and damage variable for various materials at different temperatures. Compact tension and C-shaped tension specimens are selected for the simulation of crack growth analysis. For damage evaluation, both local and nonlocal approaches are employed. The accuracy of the extended finite element method solutions is checked by comparing with experimental results and finite element solutions. These results show that the extended finite element method requires a much coarser mesh to effectively model crack propagation. It is also shown that mesh independent results can be achieved by using nonlocal implementation.
“…A continuum domain (Ω) bounded by boundary (Γ) is partitioned into boundary (Γt) with prescribed traction, traction free boundaries (Γs), and boundary (Γu) with prescribed displacement as shown in Figure 1. The equilibrium equations along with boundary conditions are given as (Kumar et al., 2016; Singh et al., 2017) where σ is the stress tensor, n is the unit normal vector, b represents the body force per unit volume, u is the displacement field vector, and t¯ represents the traction vector. Figure 1.Two-dimensional homogeneous body.…”
Section: Mathematical Formulationmentioning
confidence: 99%
“…Application of Gauss quadrature in enriched element subtriangularization technique is quite popular. While performing subtriangularization the number of Gauss points and their location changes in an element (Kumar et al., 2016). As per equation (7), the damage is calculated at the Gauss points and if the position and number of these Gauss points change with crack advancement, it will be cumbersome to evaluate the damage variable properly.…”
Section: Mathematical Formulationmentioning
confidence: 99%
“…Both local and nonlocal approaches are used. The iterative scheme for creep crack growth simulation is as follows (Hsu and Zhai, 1984; Kumar et al., 2016; Levy, 1981) For a given mesh and crack position, at time t=0, initialize damage variable ω=0and change in stress Δσ=0 at each Gauss point.Elasto-plastic analysis, Perform elasto-plastic analysis by assuming that at a material point, the state of stress at step i is known. So the known quantities are id,iε,iσ,iCe.Apply the incremental external force vector Δfext and calculate the total external force for the current load step (i+1) as Initialize the variables j-1i+1d,j-1i+1ε,…”
Section: Numerical Implementationmentioning
confidence: 99%
“…A theta projection model for creep behavior was established by Evans and Wilshire (1985). Further, Kumar et al. (2016) modified the theta projection method to improve the accuracy of modeling.…”
In the present work, elasto-plastic creep crack growth simulations are performed using continuum damage mechanics and extended finite element method. Liu–Murakami creep damage model and explicit time integration scheme are used to evaluate the creep strain and damage variable for various materials at different temperatures. Compact tension and C-shaped tension specimens are selected for the simulation of crack growth analysis. For damage evaluation, both local and nonlocal approaches are employed. The accuracy of the extended finite element method solutions is checked by comparing with experimental results and finite element solutions. These results show that the extended finite element method requires a much coarser mesh to effectively model crack propagation. It is also shown that mesh independent results can be achieved by using nonlocal implementation.
“…Temperature is an important factor for creep. Selecting reasonable materials with good thermal stability can prevent creep when working in the high temperature, simultaneously avoiding the fluctuation of temperature[20][21].…”
Two‐step stress‐aging tests, as well as pre‐treatment plus stress‐aging experiments, are performed on a 7075 aluminum (Al–Zn–Mg–Cu) alloy. Influences of stress‐aging parameters on mechanical behavior and fracture mechanism are investigated through uniaxial tensile test and fracture morphology analysis. It is revealed that the stress‐aging dramatically influences the mechanical properties and fracture characteristics of the studied alloy, which is contributed to the sensitivity of microstructures to stress‐aging. When the alloy undergoes two‐step stress‐aging, the ultimate tensile strength and yield strength first increase and then decrease with the increased first step stress‐aging temperature, while the elongation first decreases and then increases. For the retrogression pre‐treated plus stress‐aged alloy, the yield strength first increases and then drops with the increased retrogression pre‐treatment time, while the ultimate tensile strength almost remains stable. Furthermore, the elongation continuously increases with the increased retrogression pre‐treatment time. The observation of fracture morphology indicates that the dimple‐type intergranular fracture is the main fracture mechanism for the two‐step stress‐aged and retrogression pre‐treated plus stress‐aged alloys.
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