Lode angle dependency due to anisotropic damage

International Journal of Damage Mechanics ◽

10.1177/1056789520948563 ◽

2020 ◽

pp. 105678952094856

Author(s):

A Mattiello ◽

R Desmorat

Keyword(s):

Plastic Strain ◽

Damage Evolution ◽

Time Integration ◽

Anisotropic Damage ◽

Proportional Loading ◽

Isotropic Materials ◽

Damage Models ◽

Evolution Laws ◽

Lode Angle ◽

Fully Coupled

The lode angle dependency introduced by anisotropic damage evolution laws is analyzed in detail for initially isotropic materials. Many rupture criteria are obtained, under the proportional loading assumption, by the time integration of different anisotropic damage evolution laws [Formula: see text] among the three existing families: strain governed, stress governed and plastic strain governed. The cross-analysis of path independent rupture criteria and of anisotropic damage evolution laws finally allows us to improve the Lode angle dependency of (fully coupled) anisotropic damage models.

Download Full-text

Failure Predictions for DP Steel Cross-die Test using Anisotropic Damage

International Journal of Damage Mechanics ◽

10.1177/1056789511407646 ◽

2011 ◽

Vol 21 (5) ◽

pp. 713-754 ◽

Cited By ~ 18

Author(s):

M. S. Niazi ◽

H. H. Wisselink ◽

T. Meinders ◽

J. Huétink

Keyword(s):

Strain Rate ◽

Damage Evolution ◽

Damage Model ◽

Anisotropic Damage ◽

Continuum Damage ◽

Anisotropic Plasticity ◽

Continuum Damage Model ◽

Damage Models ◽

Isotropic Damage ◽

Failure Predictions

The Lemaitre's continuum damage model is well known in the field of damage mechanics. The anisotropic damage model given by Lemaitre is relatively simple, applicable to nonproportional loads and uses only four damage parameters. The hypothesis of strain equivalence is used to map the effective stress to the nominal stress. Both the isotropic and anisotropic damage models from Lemaitre are implemented in an in-house implicit finite element code. The damage model is coupled with an elasto-plastic material model using anisotropic plasticity (Hill-48 yield criterion) and strain-rate dependent isotropic hardening. The Lemaitre continuum damage model is based on the small strain assumption; therefore, the model is implemented in an incremental co-rotational framework to make it applicable for large strains. The damage dissipation potential was slightly adapted to incorporate a different damage evolution behavior under compression and tension. A tensile test and a low-cycle fatigue test were used to determine the damage parameters. The damage evolution was modified to incorporate strain rate sensitivity by making two of the damage parameters a function of strain rate. The model is applied to predict failure in a cross-die deep drawing process, which is well known for having a wide variety of strains and strain path changes. The failure predictions obtained from the anisotropic damage models are in good agreement with the experimental results, whereas the predictions obtained from the isotropic damage model are slightly conservative. The anisotropic damage model predicts the crack direction more accurately compared to the predictions based on principal stress directions using the isotropic damage model. The set of damage parameters, determined in a uniaxial condition, gives a good failure prediction under other triaxiality conditions.

Download Full-text

Using ultrasonic investigations to develop anisotropic damage models for initially transverse isotropic materials undergoing damage to remain transverse isotropic

International Journal of Solids and Structures ◽

10.1016/j.ijsolstr.2018.01.007 ◽

2018 ◽

Vol 138 ◽

pp. 155-165 ◽

Cited By ~ 9

Author(s):

Louise Olsen-Kettle

Keyword(s):

Anisotropic Damage ◽

Isotropic Materials ◽

Damage Models ◽

Transverse Isotropic

Download Full-text

Numerical integration of elasto-plasticity coupled to damage using a diagonal implicit Runge–Kutta integration scheme

International Journal of Damage Mechanics ◽

10.1177/1056789511433341 ◽

2012 ◽

Vol 22 (1) ◽

pp. 68-94 ◽

Cited By ~ 8

Author(s):

Eric Borgqvist ◽

Mathias Wallin

Keyword(s):

Numerical Integration ◽

Damage Evolution ◽

Finite Strain ◽

Integration Scheme ◽

Euler Scheme ◽

Implicit Euler Scheme ◽

Damage Models ◽

Integration Schemes ◽

Evolution Laws ◽

Runge Kutta

This article is concerned with the numerical integration of finite strain continuum damage models. The numerical sensitivity of two damage evolution laws and two numerical integration schemes are investigated. The two damage models differ in that one of the models includes a threshold such that the damage evolution is suppressed until a certain effective plastic strain is reached. The classical integration scheme based on the implicit Euler scheme is found to suffer from a severe step-length dependence. An alternative integration scheme based on a diagonal implicit Runge--Kutta scheme originally proposed by Ellsiepen ( 1999 ) is investigated. The diagonal implicit Runge--Kutta scheme is applied to the balance of momentum as well as the constitutive evolution equations. When applied to finite strain multiplicative plasticity, the diagonal implicit Runge--Kutta scheme destroys the plastic incompressibility of the underlying continuum evolution laws. Here, the evolution laws are modified such that the incompressibility of the plastic deformation is preserved approximately. The presented numerical examples reveal that a significant increase in accuracy can be obtained at virtually no cost using the diagonal implicit Runge--Kutta scheme. It is also shown that for the model including a discontinuous evolution law, the superiority of the diagonal implicit Runge--Kutta scheme over the implicit Euler scheme is reduced.

Download Full-text

A Study on the Coupled Thermal and Damage Effects in Deforming Solids

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.312-315.229 ◽

2011 ◽

Vol 312-315 ◽

pp. 229-234

Author(s):

M. Vaz ◽

Pablo A. Muñoz-Rojas ◽

M.R. Lange

Keyword(s):

Metal Forming ◽

Ductile Failure ◽

Tensile Tests ◽

Thermal Softening ◽

Mechanical Degradation ◽

Material Behaviour ◽

Temperature Variations ◽

Damage Models ◽

Notched Specimens ◽

Fully Coupled

Mechanical degradation and ductile failure in metal forming operations can be successfully modelled using fully coupled damage models. In addition, it has been largely reported in the literature that temperature variations affect material behaviour, especially thermal softening. This paper presents a numerical discussion of the coupled effects between ductile damage and temperature evolution based on the simulation of tensile tests of notched specimens.

Download Full-text

On the non-conservativeness of a class of anisotropic damage models with unilateral effects

Comptes Rendus Mécanique ◽

10.1016/j.crme.2006.05.006 ◽

2006 ◽

Vol 334 (7) ◽

pp. 414-418 ◽

Cited By ~ 13

Author(s):

Noël Challamel ◽

Damien Halm ◽

André Dragon

Keyword(s):

Anisotropic Damage ◽

Damage Models ◽

Unilateral Effects

Download Full-text

Plastic strain induced damage evolution and martensitic transformation in ductile materials at cryogenic temperatures

10.1063/1.1472540 ◽

2002 ◽

Cited By ~ 1

Author(s):

C. Garion

Keyword(s):

Martensitic Transformation ◽

Plastic Strain ◽

Damage Evolution ◽

Cryogenic Temperatures ◽

Ductile Materials

Download Full-text

Comparison of Two Time-Integration Algorithms for an Anisotropic Damage Model Coupled with Plasticity

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.784.292 ◽

2015 ◽

Vol 784 ◽

pp. 292-299 ◽

Cited By ~ 1

Author(s):

Stephan Wulfinghoff ◽

Marek Fassin ◽

Stefanie Reese

Keyword(s):

Evolution Equations ◽

Damage Model ◽

Time Integration ◽

Three Dimensional ◽

Anisotropic Damage ◽

Euler Scheme ◽

The Finite Element Method ◽

Time Step ◽

Implicit Euler Scheme ◽

Integration Algorithms

In this work, two time integration algorithms for the anisotropic damage model proposed by Lemaitre et al. (2000) are compared. Specifically, the standard implicit Euler scheme is compared to an algorithm which implicitly solves the elasto-plastic evolution equations and explicitly computes the damage update. To this end, a three dimensional bending example is solved using the finite element method and the results of the two algorithms are compared for different time step sizes.

Download Full-text

Damaged behavior under plane stress

European Journal of Computational Mechanics ◽

10.13052/ejcm.20.341-368 ◽

2011 ◽

pp. 341-368

Author(s):

Thomas Paris ◽

Khémaïs Saanouni

Keyword(s):

Plane Stress ◽

Constitutive Equations ◽

Stress Condition ◽

Time Integration ◽

Reference Case ◽

Plane Stress Condition ◽

Integration Schemes ◽

Hyperbolic Sine ◽

Time Integration Schemes ◽

Fully Coupled

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.

Download Full-text