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Limits of isotropic damage models for complex load paths -- beyond stress triaxiality and Lode angle parameter

K. Feike, P. Kurzeja, J. Mosler, K. Langenfeld

TL;DR

The paper critically assesses whether isotropic damage modeling based on stress triaxiality, Lode angle parameter, and equivalent plastic strain suffices to predict ductile damage under complex load paths. By employing two prototype models (ECC and LEM) in isotropic and anisotropic forms and calibrating them to a common steel (16MnCrS5), it systematically analyzes load-path dependence through path parametrization and optimization. The results show that even with controlled invariants, damage evolution is not uniquely determined; optimized load paths can yield substantially different final damage or stiffness, and fracture-surface analyses reveal significant deviations up to about 30% in plastic strain for non-proportional paths. Overall, the work demonstrates the necessity for richer damage descriptions beyond $(\eta, \bar{\theta}, \varepsilon^{\mathrm{p,eq}})$, with implications for forming-process modeling and experimental validation.

Abstract

The stress triaxiality and the Lode angle parameter are two well established stress invariants for the characterization of damage evolution. This work assesses the limits of this tuple by using it for damage predictions in a continuum damage mechanics framework. Isotropic and anisotropic formulations of two well-established models are used to avoid model-specific restrictions. The damage evolution is analyzed for different load paths, while the stress triaxiality and the Lode angle parameter are controlled. The equivalent plastic strain is moreover added as a third parameter, but still does not suffice to uniquely define the damage state. As a consequence, well-established concepts such as fracture surfaces depending on this triple have to be taken with care, if complex paths are to be investgated. These include, e.g., load paths observed during metal forming applications with varying load directions or multiple stages.

Limits of isotropic damage models for complex load paths -- beyond stress triaxiality and Lode angle parameter

TL;DR

The paper critically assesses whether isotropic damage modeling based on stress triaxiality, Lode angle parameter, and equivalent plastic strain suffices to predict ductile damage under complex load paths. By employing two prototype models (ECC and LEM) in isotropic and anisotropic forms and calibrating them to a common steel (16MnCrS5), it systematically analyzes load-path dependence through path parametrization and optimization. The results show that even with controlled invariants, damage evolution is not uniquely determined; optimized load paths can yield substantially different final damage or stiffness, and fracture-surface analyses reveal significant deviations up to about 30% in plastic strain for non-proportional paths. Overall, the work demonstrates the necessity for richer damage descriptions beyond , with implications for forming-process modeling and experimental validation.

Abstract

The stress triaxiality and the Lode angle parameter are two well established stress invariants for the characterization of damage evolution. This work assesses the limits of this tuple by using it for damage predictions in a continuum damage mechanics framework. Isotropic and anisotropic formulations of two well-established models are used to avoid model-specific restrictions. The damage evolution is analyzed for different load paths, while the stress triaxiality and the Lode angle parameter are controlled. The equivalent plastic strain is moreover added as a third parameter, but still does not suffice to uniquely define the damage state. As a consequence, well-established concepts such as fracture surfaces depending on this triple have to be taken with care, if complex paths are to be investgated. These include, e.g., load paths observed during metal forming applications with varying load directions or multiple stages.
Paper Structure (18 sections, 41 equations, 12 figures, 2 tables)

This paper contains 18 sections, 41 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Continuum damage mechanics -- two prototype models
  3. ECC-Model -- Effective Configuration Concept
  4. LEM-Model -- Effective Stress Concept (Lemaitre model)
  5. Similarities and differences between the prototype damage models
  6. Model calibration with case-hardened steel 16MnCrS5
  7. Finite element simulations of a tension-torsion test
  8. Methodology of evaluation: load path parametrization and damage measures
  9. Parametrization of load paths
  10. Characteristic damage measures and target functions
  11. Numerical examples
  12. The smaller the stress triaxiality, the smaller the damage accumulation? Coupled tension-torsion experiments
  13. Is damage accumulation uniquely governed by the triple stress triaxiality, Lode (angle) parameter and equivalent plastic strain?
  14. Fracture surfaces for proportional loading
  15. Fracture surfaces for non-proportional load paths
  16. ...and 3 more sections

Figures (12)

  • Figure 1: Experiment vs. simulation in calibration: (a) and (b) Uniaxial tensile test with sequential unloading. (c) Additional numerical shear test comparing the model predictions.
  • Figure 2: Finite element simulation of a tension-torsion test: Servohydraulic Axial - Torsional Test System and the tensile specimen (case-hardened steel 16MnCrS5) with an overly of the finite element discretization of the simulated domain with 800 axisymmetric elements.
  • Figure 3: Combined axial/torsional test: sketch of mechanical system and boundary conditions in terms of prescribed stress and strains. Prescribed coordinates are boxed. According to the underlying kinematics, $\varepsilon_{zz} = u/L$ and $\varepsilon_{\theta z} = 1/2 \, \gamma \, R/L$.
  • Figure 4: Combined axial/torsional test: (a) Final relative stiffness $\xi_\mathbb{E}(t=1)$ and (b) final equivalent plastic deformation $\varepsilon^\text{p,eq}$$(t=1)$ for all four constitutive models and for the reference load path (left bars) as well as for the optimized load path (right bars). (c) Evolution of effective relative stiffness $\xi_\mathbb{E}$ in terms of $\varepsilon^\text{p,eq}$.
  • Figure 5: Combined axial/torsional test: Reference and optimized load paths for different ductile damage models. Reference paths are represented by dotted lines, optimized load paths by solid lines.
  • ...and 7 more figures

Theorems & Definitions (1)

  • Remark 1