Bilinear damage evolution in AA2011 wire drawing processes

This paper presents an experimental and numerical analysis of damage evolution in AA2011 aluminum alloy wires drawn under different scenarios. To this end, load-unload tensile tests were firstly carried out in order to characterize the degradation of the mechanical response in every cycle where the experimental results show a bilinear damage relationship in terms of the effective plastic strain. Therefore, a modification of the classical Lemaitre model is proposed in this work in order to reproduce bilinear paths of damage with the addition of only two parameters that can be directly obtained from the material characterization. Then, the damage predictive capability of this new experimental-based model is assessed in numerical simulations of the drawing process in one and two passes (considering for this last case the sequential and tandem configurations) where the computed predictions are compared with the corresponding experimental data showing a good agreement between them.

Numerical Investigation of Plastic Strain Homogeneity during Equal-Channel Angular Pressing of a Cu-Zr Alloy

A three-dimensional finite element method (3D FEM) simulation was carried out using ABAQUS/Explicit software to simulate multi-pass processing by equal-channel angular pressing (ECAP) of a circular cross-sectional workpiece of a Cu-Zr alloy. The effective plastic strain distribution, the strain homogeneity and the occurrence of a steady-state zone in the workpiece were investigated during ECAP processing for up to eight passes. The simulation results show that a strain inhomogeneity was developed in ECAP after one pass due to the formation of a corner gap in the outer corner of the die. The calculations show that the average effective plastic strain and the degree of homogeneity both increase with the number of ECAP passes. Based on the coefficient of variance, a steady-state zone was identified in the middle section of the ECAP workpiece, and this was numerically evaluated as extending over a length of approximately 40 mm along the longitudinal axis for the Cu-Zr alloy.

An improved monolithic Newton-Raphson scheme for solving plastic flow with nonlinear flow laws

<p>Brittle-plastic flows where the yield strength is a decreasing, non-linear function of plastic strain are thought to be commonplace in the Earth, and responsible for some of its most catastrophic events. Recent work [1] has highlighted again the computational benefit of an iterative Newton-Raphson scheme that contains a linearization of the plastic flow problem that is consistent with its time discretization. However, such a consistent linearization requires a nested set of iterations to converge on a yield strength if it is governed by a law that is non-linear in strain (or strain rate).</p><p>Eckert and co-authors [2] have shown that the construction of a consistent linearization can be avoided altogether, including these inner iterations, though at the considerable cost of including the full plastic strain tensor as an objective variable alongside the displacement vector. The resulting system is therefore larger, but as it can be expressed directly, posesses the quality that it may be linearized automatically, cheaply, and accurately by finite-differencing the non-linear residual with respect to the solution variables. Their algorithm naturally incorporates predictor and corrector polynomials that are second-order accurate in time, contrasting with traditional methods that are often derived using a Backward Euler time integrator. We present a modification to this algorithm that suppresses the cost of operating it significantly by replacing the symmetric second-order plastic strain tensor with a single effective plastic strain scalar objective variable, cutting the number of unknowns by 40% (2D) and 55% (3D) This makes it computationally more on par with existing schemes that employ a consistent tangent modulus.</p><p>We demonstrate this improved algorithm with test cases of non-linear strain softening laws relevant to Earth scientists, that include regularization by both Kelvin visco-plasticity [3] and non-local measures of effective plastic strain [4]. In addition, we analyse performance of this scheme with respect to existing algorithms.</p><p><em>References</em><br>[1] Duretz et al. (2018). “The benefits of using a consistent tangent operator for viscoelastoplastic computations in geodynamics.” <em>Geochemistry, Geophysics, Geosystems</em>, 19, 4904–4924.</p><p>[2] Eckert et al. (2004). “A BDF2 integration method with step size control for elasto-plasticity.” <em>Computational Mechanics</em> 34.5, 377–386.</p><p>[3] Duretz et al. (2019). “Finite Thickness of Shear Bands in Frictional Viscoplasticity and Implications for Lithosphere Dynamics.” <em>Geochemistry, Geophysics, Geosystems</em>, 20, 5598–5616.</p><p>[4] Engelen et al. (2003). “Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour.” <em>International Journal of Plasticity</em><br>19.4, 403–433.</p>

Fatigue behavior of trabecular bone orientation

The present study reports the anisotropy effects of uniaxial and multiaxial loading on cancellous bone in order to mimic true physiological conditions as well as pathological reactions and thereby provides improved data that represents clinical and real life conditions. Cancellous bone samples were CT-scanned for morphological analysis and model construction. The models were then computationally loaded on three different directions; horizontal, vertical, and at 45°. Lower BV/TV, Tb.Th, and Conn.D resulted in lower number of cycles to failure, regardless to the loading conditions. However, the number of cycles to failure was found to be negatively correlated to the value of structural model index. Dramatic increased in effective plastic strain and decrease in cycles to failure were demonstrated by the cancellous bone models under multiaxial loading. The reduction of fatigue life was five times lower in multiaxial condition in comparison to the fatigue life under uniaxial loading. Off-axis orientation effect on the fatigue life of the trabecular bone was demonstrated the worst in horizontal trabecular bone model. Effective plastic strain was recorded the highest in horizontal model, while the model at 45° demonstrated 1.6 times higher effective plastic strain than the vertical ones. This is due to several numbers of thin trabeculae which are susceptible to fatigue at higher stress concentration. In conclusion, the anisotropic effect of uniaxial and multiaxial loading onto the mechanical behaviour of bovine cancellous bone was demonstrated throughout this study. It is apparent that multiaxial with off-axis forces are important to be considered as the loading direction manifests the fatigue lifetime of cancellous bone.

Effect of hardening law and process parameters on finite element simulation of single point incremental forming (SPIF) of 7075 aluminum alloy sheet

In the last two decades, the advances of using computers in sheet metal forming processes have introduced a novel adjustable process known as incremental sheet forming (ISF) as an optimal method for fast prototyping and low numbers of production. Formability and deformation behavior of ISF process are highly affected by the selected process parameters, such as the toolpath, step size, tool diameter, feed rate, and lubrication. The purpose of this work was to study the effect of these process parameters as well as hardening law on single point incremental forming (SPIF) process. For this work, a truncated-cone geometry was considered as a target shape with 7075-O aluminum alloy sheets. The simulations were conducted with different process parameters, i.e., toolpath type, step size, tool size, feed rate, friction coefficient, and wall angle with respect to the tool force and moment, effective plastic strain distribution and thickness of the part. In addition, three types of hardening laws i.e., isotropic extended Voce type hardening law, combined isotropic-kinematic Chaboche type hardening laws with single and double back-stress terms were applied in the finite element simulation of SPIF process. A detailed comparison of these hardening laws' predictions was made with respect to the tool force and moment, effective plastic strain distribution and thickness of the part.

Estimation of the Onset of Crack Growth in Ductile Materials

In this paper, the ductile fracture mechanism is discussed. The results of numerical and experimental analyses were used to estimate the onset of crack front growth. It was assumed that the ductile fracture in front of the crack starts at the location along the crack front where the accumulated effective plastic strain reaches a critical value. According to numerous research articles, the critical effective plastic strain depends on the stress triaxiality and the Lode angle. The experimental program was performed using five different specimen geometries, three different materials, and three different temperatures of +20 °C, −20 °C, and −50 °C. Using the experimental data and results of the finite element computations, the critical effective plastic strains were determined for each material and temperature. However, before the critical effective plastic strain was determined, a careful calibration of the stress–strain curves was performed after modification of the Bai–Wierzbicki procedure. It was found that critical effective plastic strain was a function of triaxiality factor and Lode parameter, as expected, and that the fracture locus was useful to estimate the onset of ductile crack growth.

Estimation of the Onset of Crack Growth in Ductile Materials

In this paper, the ductile fracture mechanism is discussed. The results of the numerical and experimental analyses are used to estimate of the onset of the crack front growth . It is assumed that the ductile fracture in front of the crack starts at the location along the crack front where the accumulated effective plastic strain reaches a critical value. It is also assumed that the critical effective plastic strain depends on the stress triaxiality and the Lode angle. The experimental programme was performed using five different specimen geometries, three different materials and three different temperatures of +20°C, -20°C and -50°C. Using the experimental data and the results of the finite element computations, the critical effective plastic strains are determined for each material and each temperature. However, before the critical effective plastic strain is determined, a careful calibration of the stress–strain curves was performed after modification of the Bai–Wierzbicki procedure. Finally, by analysing the experimental results recorded during the interrupted fracture tests and scanning microscopy observations, the research hypothesis is verified.

Elasto-plastic analysis of the contact region between a rigid ellipsoid and a semi-flat surface

When the load acting on a mechanical structure is greater than the yield strength of the material, the contact surface will undergo plastic deformation. Cumulative plastic deformation has an important influence on the lifespan of mechanical parts. This article presents a three-dimensional semi-analytical model based on the conjugate gradient method and fast Fourier transform algorithm, with the aim of studying the characteristic parameters of the contact region between a rigid ellipsoid and elasto-plastic half-space. Moreover, normal forces and tangential traction were considered, as well as the contact pressure resulting from various sliding speeds and friction coefficients. The contact pressure, effective plastic strain, von Mises stress, and residual stress were measured and shown to increase with increasing sliding velocity. Finally, when the friction coefficient, contact pressure, and effective plastic strain are increased, the von Mises stress is also shown to increase, whereas the residual stress decreases.