A stress-state-dependent damage criterion for metals with plastic anisotropy

Abstract

The paper discusses the effect of stress state and of loading direction on the onset and evolution of damage in anisotropic ductile metals. A series of experiments with uniaxially and biaxially loaded specimens covering a wide range of stress states and different loading directions is used in combination with corresponding numerical simulations to develop damage criteria. The underlying continuum damage model is based on kinematic definition of damage tensors. The strain rate tensor is additively decomposed into elastic, plastic and damage parts. The anisotropic plastic behavior of the investigated aluminum alloy sheets is governed by the Hoffman yield condition taking into account the strength-differential effect revealed by uniaxial tension and compression tests. Based on this yield criterion generalized anisotropic stress invariants as well as the generalized stress triaxiality and the generalized Lode parameter are defined characterizing the stress state in the anisotropic ductile metal. A damage criterion formulated in terms of these anisotropic stress invariants is proposed and damage mode parameters allow adequate consideration and combination of different damage processes on the micro-level. At the onset of damage the anisotropic stress parameters are determined. With these experimental-numerical data the damage mode parameters are identified depending on stress state and loading direction.

Analysis of effects of material anisotropy on ductile damage using microscopic unit‐cell model

“…The stress invariants are newly defined using the Hoffman yield criterion. The determination of elastic and plastic anisotropic parameters can be found in detail in Brünig et al [17]. The first stress invariant is described as…”

“…where 𝐼 𝐻 1 and 𝐽 𝐻 2 are the generalized stress invariants defined with respect to damaged configurations and 𝜎 is the equivalent damage stress. 𝛼 and are stress-state-and loading-direction-dependent parameters, which have been identified using an experimental and numerical procedure as in Brünig et al [17]. Furthermore, the evolution of the damage strains is given by the damage rule as…”

“…The determination of elastic and plastic anisotropic parameters can be found in detail in Brünig et al. [17]. The first stress invariant is described as $$$$\begin{equation} {\bar{I}}^H_1 = \frac{1}{a} {\bf C} \cdot {\bar{{\bf T}}} \;\;\;{\rm with} \; \; \; a = \frac{1}{3} \; {\rm tr} {\bf C} \end{equation}$$$$whereas the second and the third deviatoric stress invariants are given by $$$$\begin{equation} {\bar{J}}^H_2 = \frac{1}{2} {\bar{{\bf T}}} \cdot {\it \text{{\bf D}}}\, {\bar{{\bf T}}} \end{equation}$$$$and $$$$\begin{equation} {\bar{J}}^H_3 = {\rm det} {\left({\it \text{{\bf D}}} \; {\bar{{\bf T}}} \right)}.$$…”

“…α and β are stress‐state‐ and loading‐direction‐dependent parameters, which have been identified using an experimental and numerical procedure as in Brünig et al. [17]. Furthermore, the evolution of the damage strains is given by the damage rule as $$$$\begin{equation} \dot{\text{{\bf H}}}\vphantom{\text{{\bf H}}}^{da} = \dot{\mu } {\left(\frac{\tilde{\alpha }}{\sqrt {3}}\text{{\bf 1}} + \tilde{\beta }{\text{{\bf N}}} \right)} \end{equation}$$$$where $$\tilde{\alpha }$$ and $$\tilde{\beta }$$ are scalar parameters dependent on the stress‐state and loading direction.…”

Chemical Corrosion-Water-Confining Pressure Coupling Damage Constitutive Model of Rock Based on the SMP Strength Criterion

“…The integration of a constitutive model holds utmost importance in the framework of rock mechanics’ strength theory. Significant progress and achievements have been made in the theory of rock damage by researchers both domestically and internationally [ 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. Rocks typically exhibit robust coupling properties as a result of the interplay between geological processes and intricate natural surroundings over extended periods.…”