Evolution of Strength Parameters for Sandstone Specimens during Triaxial Compression Tests

Despite the lack of test data of the coefficient of pressure sensitivity α and the shearing cohesion k, the Drucker–Prager criterion is commonly applied for numerical analyses of geotechnical engineering. To bridge the gap between the wide application and insufficient knowledge of strength parameters of the Drucker–Prager criterion, this study presents experimentally calibrated strength parameters of this criterion for the first time. This paper proposes a new method to measure α and k in the Drucker–Prager criterion. The square root of the second invariant of the deviatoric stress tensor J 2 is linearly fitted with the first invariant of the stress tensor I 1 in the stress space. The parameters φ and c in the Mohr–Coulomb criterion and α and k in the Drucker–Prager criterion are calibrated to the same set of triaxial compression tests of sandstones. With these testing results, five pairs of conversion formulae (which are most commonly used in the literature) are examined and the most appropriate pair of conversion formulae is identified. With parameters indicating cohesive strength (c and k) and parameters indicating frictional strength ( φ and α ), the evolutions of different strength components are compared with those in the cohesion-weakening friction-strengthening model. With an increase in plastic deformation, the cohesive strength parameters c and k firstly increase to a peak value and then decrease. The frictional strength parameters φ and α gradually increase at a decreasing rate after the initial yield point.

A Cartesian Scheme for Compressible Multimaterial Hyperelastic Models with Plasticity

We describe a numerical model to simulate the non-linear elasto-plastic dynamics of compressible materials. The model is fully Eulerian and it is discretized on a fixed Cartesian mesh. The hyperelastic constitutive law considered is neohookean and the plasticity model is based on a multiplicative decomposition of the inverse deformation tensor. The model is thermodynamically consistent and it is shown to be stable in the sense that the norm of the deviatoric stress tensor beyond yield is non increasing. The multimaterial integration scheme is based on a simple numerical flux function that keeps the interfaces sharp. Numerical illustrations in one to three space dimensions of high-speed multimaterial impacts in air are presented.

About Error Calculation in X-Ray Stress Measurement

It is shown that the knowledge of standard deviations (Δσij) of the components of a stress tensor (σij) is not sufficient to calculate also standard deviations of quantities derived from the stress tensor, as principal stresses (σI, σII, σIII), von Mises stress, Tresca stress, and the components of the deviatoric stress tensor σ'ij. For such a calculation one needs all information about the measurement and the method for the calculation of σij. This information is: the accuracy of each measured lattice plane distance and the x-ray elastic factors Fij(φ,ψ,hkl) of each measured point. Equations are given for the calculation of the standard deviations of all the mentioned quantities. For special cases of measurement strategy the wanted calculations become easier. This is also given.

Asymmetric Yield Locus Evolution for HCP Materials: A Continuum Constitutive Modeling Approach

A continuum-based plasticity approach is considered to model the anisotropic hardening response of hexagonal closed packed (hcp) materials. A Cazacu-Plunkett-Barlat (CPB06) yield surface is modified to create anisotropic hardening in terms of the accumulated plastic strain. The anisotropy and asymmetry parameters are replaced with saturation-type functions and the new modified model is then optimized globally to fit the material response. Furthermore, the effect of the number of linear stress transformations performed on the deviatoric stress tensor is investigated on the capability of the model to capture the response from the experiments. By increasing the number of stress transformations, more flexibility is obtained. However, increasing the number of stress transformations increases the arithmetic calculations involved in the material model. The proposed approach is an effective and time efficient method to create material models with complex evolving tension/compression behavior.

Residual Stress Analysis of the Autofrettaged Thick-Walled Tube Using Nonlinear Kinematic Hardening

Recent research indicates that accurate material behavior modeling plays an important role in the estimation of residual stresses in the bore of autofrettaged tubes. In this paper, the material behavior under plastic deformation is considered to be a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. The yield surface is assumed to depend on the first stress invariant and the Lode angle parameter which is defined as a function of the second and the third invariants of the deviatoric stress tensor. Furthermore for estimating the unloading behavior, the Chaboche's hardening evolution equation is modified. These modifications are implemented by adding new terms that include the effect of the first stress invariant and pervious plastic deformation history. For evaluation of this unloading behavior model a series of loading-unloading tests are conducted on four types of test specimens which are made of the high-strength steel, DIN 1.6959. In addition finite element simulations are implemented and the residual stresses in the bore of a simulated thick-walled tube are estimated under the autofrettage process. In estimating the residual stresses the effect of the tube end condition is also considered.

Characterization of Ductile Failure Behavior of the Ferritic Steel Using Damage Mechanics Modeling Approach

A ductile failure is characterized by pronounced plastic deformations which involve significant plastic strains. The modeling of this failure behavior requires a precise description of the material plasticity starting from the crack initiation, its propagation through the material to the final fracture. The classical theory of metal plasticity based on the von Mises or Tresca formulations assumes that the effect of hydrostatic pressure on the flow potential is insignificant. Furthermore, it postulates that the flow stress is independent of the third stress invariant of the deviatoric stress tensor. The scientific findings from last few years show, however, that these both quantities should be considered for the precise description of plasticity, especially, of the real materials [1-4].

APPLICATION OF THE PLASTICITY MODELS THAT INVOLVE THREE STRESS INVARIANTS

Increasing experimental evidence shows that the classical J2 plasticity theory may not fully describe the plastic response of many materials, including some metallic alloys. In this paper, the effect of stress state on plasticity and the general forms of the yield function and flow potential for isotropic materials are assumed to be functions of the first invariant of the stress tensor (I1) and the second and third invariants of the deviatoric stress tensor (J2 and J3). A 5083 aluminum alloy, Nitronic 40 (a stainless steel), and Zircaloy-4 (a zirconium alloy) were tested under tension, compression, torsion, combined torsion–tension and combined torsion–compression at room temperature to demonstrate the applicability of a proposed I1-J2-J3 dependent model. The I1-J2-J3 dependent plasticity model was implemented in ABAQUS via a user defined subroutine. The model parameters were determined and validated by comparing the numerically predicted and experimentally measured load versus displacement and/or torque versus twist angle curves. The results showed that the proposed model incorporating the I1-J2-J3 dependence produced output that matched experimental data more closely than the classical J2 plasticity theory for the loading conditions and materials tested.