An anisotropic theory of continuum damage mechanics for ductile fracture

doi:10.1016/0013-7944(87)90108-1

Engineering Fracture Mechanics

Volume 27, Issue 5, 1987, Pages 547-558

https://doi.org/10.1016/0013-7944(87)90108-1 Get rights and content

Abstract

The development of an anisotropic theory of continuum damage mechanics for ductile fracture is described. A new anisotropic damage evolution equation and a constitutive equation of plasticity are formulated using a damage effect tensor $M(D)$ proposed recently by the authors. This is followed by the development of a generalized damage characteristic tensor $J$ to characterize anisotropic damage evolution which is shown to be compatible with the damage effect tensor. The tensorial equation of damage evolution for the proposed tensor $J$ can be reduced to a scalar equation if the damage state is isotropic. Verification of the proposed model has been performed by conducting simple tension tests and the results are shown to be satisfactory.

References (27)

G.C. Sih et al.
Fracture initiation under gross yielding: strain energy density criterion
Engng Fracture Mech.
(1983)
C.L. Chow et al.
Ductile crack propagation with the strain energy density criterion
Engng Fracture Mech.
(1985)
C.L. Chow et al.
Application of the strain energy density criterion to ductile fracture
J. theor. appl. Fracture Mech.
(1985)
J. Lemaitre
How to use damage mechanics
Nucl. Engng Design
(1984)
D.G.H. Latzko
Post-Yield Fracture Mechanics
(1979)
A.A. Wells
Application of fracture mechanics at and beyond general yielding
Br. Weld. J.
(1963)
F.M. Burdekin et al.
The crack opening displacement approach to fracture mechanics in yielding mechanics
J. Strain Anal.
(1966)
J.R. Rice
A path independent integral and approximate analysis of strain concentration by notches and cracks
J. appl. Mech.
(1968)
J.H. Giovanola et al.
A review of the use of the $J- integral$ as a fracture parameter
S.M. Arch
(1984)
J.H. Giovenola et al.
The crack opening displacement (COD) as a fracture parameter and a comparative assessment of COD and $J- integral$ concepts
S.M. Archs
(1984)

H.W. Liu et al.

A dual-parameter elastic-plastic fracture criterion

Int. J. Fracture

(1985)

C.L. Chow et al.

Mixed mode ductile fracture using the strain energy density criterion

Int. J. Fracture

(1985)

L.M. Kachanov

On the creep fracture time

Izv Akad. Nauk USSR Otd. Tekh.

(1958)

Cited by (408)

Interfacial constitutive model of 3D printed fiber reinforced concrete composites and its experimental validation
2024, Case Studies in Construction Materials
In recent years, 3D printing has been rapidly promoted and applied in the field of civil engineering and construction, and has been developed from landscape maintenance structures to load-bearing structures. Different from cast-in-place concrete materials, the contact interfaces between adjacent layers or filaments formed under the additive stacking process lead to distinct mechanical anisotropy of 3D printed concrete materials, and thus the mechanical model of traditional concrete materials and the design method of reinforced concrete structures are inapplicable to 3D printed concrete materials and structures. The establishment of 3D printed concrete materials is therefore of great significance to the design of 3D printed concrete structures. Currently, there is still a lack of research on the constitutive models of 3D printed fiber reinforced concrete. This study tested and analyzed the tensile and shear performances of 3D printed concrete reinforced with steel fibers and polypropylene fibers. According to the distribution porosity, the interface thickness of 3D printed fiber reinforced concrete was measured and determined. The constitutive modeling of mechanical anisotropy of 3D printed fiber-reinforced concrete were established based on the theory of damage fracture of concrete and experimental results. Results show that the interfacial tensile strength at layers and filaments of 3D printed concrete with steel fiber were 6.2 MPa and 6.9 MPa, while the capacities of 3D printed concrete with polypropylene fiber were 4.5 MPa and 4.7 MPa, respectively. The fracture damage constitutive model adopted in this study has favorable fitting degrees, which would contribute to the further finite element simulation and structural design of 3D printed concrete.
Damage and fracture initiation under shear and compression stress states in the aluminum alloy EN AW6082-T6
2024, Theoretical and Applied Fracture Mechanics
The present paper deals with the experimental and numerical analysis of damage and fracture behavior of ductile metals under combined compression and shear loading. Biaxial experiments with the H-specimen using a pneumatic downholder during compression loading and corresponding numerical simulations are discussed. A thermodynamically consistent anisotropic continuum damage model using damage strains is presented. During the experiments strain fields in critical areas of the specimens are monitored by digital image correlation (DIC) technique also showing evolution of deformation in thickness direction of thin sheets. Corresponding numerical simulations reveal the stress states and details of inelastic deformation behavior.
A gradient-extended thermomechanical model for rate-dependent damage and failure within rubberlike polymeric materials at finite strains
2024, International Journal of Plasticity
Rate-dependencies play a crucial role in the mechanical response of polymeric materials. Besides viscoelasticity, many polymers also show pronounced rate-dependent behaviour with respect to damage accumulating within the material. Furthermore, thermal effects and large deformations have to be taken into account when modelling the mechanical behaviour of polymers. Within this work, we propose a novel fully thermomechanically coupled material model for the description of rate-dependent damage combined with viscoelasticity at finite strains. The model is based on the multiplicative decomposition of the deformation gradient into thermal and mechanical parts as well as a further decomposition of the mechanical part into equilibrium and non-equilibrium contributions. To describe the temporal dependencies of the damage evolution, we make use of a Perzyna-type approach. We furthermore show the thermodynamically consistent derivation of stresses and heat sources which arise due to energy dissipations triggered by the inelastic effects within the material. With the given material formulation, we are able to describe both, damage due to creep and due to relaxation in a precise manner. Besides the theoretical aspects, we describe the numerical implementation into finite element software and present numerical studies demonstrating the capabilities of the given model.
Gradient-extended damage modelling for polymeric materials at finite strains: Rate-dependent damage evolution combined with viscoelasticity
2024, European Journal of Mechanics, A/Solids
While the strong rate-dependent effects of polymeric materials in the elastic regime are well studied, the time-dependent effects that arise in the inelastic damage regime are still difficult to model and are therefore the subject of investigation. In this work, we propose a simple but flexible formulation for the description of rate-dependent damage combined with viscoelasticity at finite strains. This model is based on a finite viscoelastic material formulation combined with a Perzyna-type approach to describe the damage evolution equation. With this formulation we are able to describe both damage due to creep and relaxation of the polymer matrix in both a qualitative and quantitative manner. Besides the main aspects of thermodynamic consistency, we describe the numerical implementation into finite elements and present numerical examples to demonstrate the capabilities of the proposed model. At last, we compare the model with experimental data and show the good predictive capabilities of this newly developed material model.
A fourth-order degradation tensor for an anisotropic damage phase-field model
2023, Forces in Mechanics
This work proposes a thermodynamically consistent phase-field model for anisotropic brittle material under the hypotheses of plane stress, small deformation and constant temperature. The model is derived from the principle of virtual power, the first and second laws of thermodynamics in the form of the Clausius-Duhem inequality. The degradation effect on the material behavior is given by a fourth-order degradation tensor introduced as an internal variable that evolves according to the current strain state rather than the conventional scalar degradation function of phase-field models. Therefore, local anisotropy can be induced, changing the material mechanical behavior differently in all directions organically. The proposed degradation tensor is defined in the global coordinate system and therefore is sensitive to any change in the principal directions of the strain and stress states. To demonstrate the model’s capability of representing damage in isotropic and transversely isotropic materials, some benchmark examples were carried out and the evolution of the damage components was analyzed.
Modeling the anisotropic behavior of highly orthotropic lithium-ion batteries polymer separators
2023, International Journal of Solids and Structures
Separators in commercial lithium-ion batteries are microporous polymeric films characterized by highly anisotropic mechanical behavior. An accurate characterization of their mechanical and fracture behavior is essential for optimal design, performance, and safety of lithium-ion batteries. In this work, the mechanical and fracture behavior of battery separators subjected to uniaxial tension and punch tests are characterized and discussed. An anisotropic continuum damage coupled elastic-hyperelastic-viscoplastic model is developed in the framework of the large deformation theory to capture the mechanical and fracture behavior of battery separators. A robust implicit integration scheme is developed then the model is implemented as a user-defined material subroutine (UMAT) in commercial finite-element software in order to solve boundary-value problems. The capability of the proposed model to predict the anisotropic mechanical behavior up to fracture for two different types of battery separators highlights the versatility of the proposed modeling approach. The model results showed a good agreement with the experimental data. Moreover, the model was able to predict the failure of the separators under different loading conditions.

View all citing articles on Scopus

^∗: Currently on leave from Huazhong University of Science & Technology, China.

View full text

An anisotropic theory of continuum damage mechanics for ductile fracture

Abstract

Engng Fracture Mech.

Engng Fracture Mech.

J. theor. appl. Fracture Mech.

Nucl. Engng Design

Post-Yield Fracture Mechanics

Application of fracture mechanics at and beyond general yielding

Br. Weld. J.

The crack opening displacement approach to fracture mechanics in yielding mechanics

J. Strain Anal.

A path independent integral and approximate analysis of strain concentration by notches and cracks

J. appl. Mech.

A review of the use of the J-integral as a fracture parameter

S.M. Arch

The crack opening displacement (COD) as a fracture parameter and a comparative assessment of COD and J-integral concepts

S.M. Archs

A dual-parameter elastic-plastic fracture criterion

Int. J. Fracture

Mixed mode ductile fracture using the strain energy density criterion

Int. J. Fracture

On the creep fracture time

Izv Akad. Nauk USSR Otd. Tekh.

A review of the use of the $J- integral$ as a fracture parameter

The crack opening displacement (COD) as a fracture parameter and a comparative assessment of COD and $J- integral$ concepts