Implementation of a Matrix Crack Spacing Parameter in a Continuum Damage Mechanics Finite Element Model

Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed

Analysis of damage and fracture formulations in cold extrusion

In forming processes, components generally undergo large deformations. This induces the evolution of damage, which can influence material and product properties. To capture these effects, a continuum damage mechanics (CDM) model, based on the work of Lemaitre [8] and Soyarslan [13, 14] as well as different fracture criteria according to Cockcroft and Latham [2], Freudenthal [4] and Oyane [10] are implemented and in- vestigated. While the CDM theory considers the evolution of damage and the associated softening, fracture criteria do not affect the results of the mechanical finite element (FE) analysis. However, a coupling is generally possible via element deletion, but material softening cannot be depicted in the simulation. Tensile tests with notched specimens are performed in order to obtain the material parameters associated with these models by inverse parameter identification processes. The optimized set of parameters is finally ap- plied to the damage and fracture models used for the FE simulations of a cold extrusion process, which are investigated in terms of damage evolution and material failure. It is demonstrated that the CDM model predicts the evolution of damage observed for differ- ent process parameters in cold extrusion quantitatively. The prediction of the failure by the fracture criteria does not agree well with the experiments

Application of the continuum damage mechanics model in the three point bending test of Ti-6Al-4V titanium alloy specimens

One of the most important and challenging activities in the simulation of the mechanical behaviour of materials is the prediction of the failure phenomena. If well calibrated, damage models can simulate and predict the failure of materials in a generalized way allowing the replication of not only the calibration tests themselves but also of different loading cases. Generally damage models can be categorized into three different groups including phenomenological models, porosity models and continuum damage mechanics (CDM) models. Different CDM models have been proposed by researchers and these models have been applied in diverse loading conditions, geometries and materials. However the limitations and advantages of the CDM models are still not completely explored in the application areas. In this paper, a CDM model, (previously calibrated with round smooth specimen) has been applied in a three-point bending test model in order to simulate the correlated experiment. Specifically, the CDM framework has been applied in a finite element model and the obtained results have been compared with the experimental data. The tested material is Ti-6Al-4V titanium alloy, which is a widely used material in the aerospace industry because of its high strength and low density. Load-displacement data in the experiments and numerical simulations are the main results, which have been compared. Therefore, the ability of the CDM model to simulate the three point bending test has been investigated and the results are discussed

A micro-mechanically based continuum damage model for fatigue life prediction of filled rubbers

International audienceThis paper presents a continuum damage model based on two mechanisms: decohesion between fillers and matrix at a micro-scale followed by a crack nucleation at a macro-scale. That scenario was developed considering micro observations conduced with a SEM and an original experimental procedure based on simple shear and tension specimens. Damage accumulation is related to fatigue life using the continuum damage mechanics (CDM). The material behavior is investigated using the statistical framework introduced by Martinez et al. (2011). A Finite Element implementation is proposed and some numerical examples are provided

Analysis of damage in high strength steels

In continuum damage mechanics (CDM) approach, damage accumulation takes place through void initiation, growth and coalescence. In this study, a Bayesian Neural Network based model has been developed to calculate the complex relationship between the extent of damage accumulation and its influencing parameters for a variety of high strength low alloy steels. The model has been applied to confirm that the predictions are reasonable

Experimental techniques for ductile damage characterisation

Ductile damage in metallic materials is caused by the nucleation, growth and coalesce of voids and micro-cracks in the metal matrix when it is subjected to plastic strain. A considerable number of models have been proposed to represent ductile failure focusing on the ultimate failure conditions; however, only some of them study in detail the whole damage accumulation process. The aim of this work is to review experimental techniques developed by various authors to measure the accumulation of ductile damage under tensile loads. The measurement methods reviewed include: stiffness degradation, indentation, microstructure analysis, ultrasonic waves propagation, X-ray tomography and electrical potential drop. Stiffness degradation and indentation techniques have been tested on stainless steel 304L hourglass-shaped samples. A special interest is placed in the Continuum Damage Mechanics approach (CDM) as its equations incorporate macroscopic parameters that can represent directly the damage accumulation measured in the experiments. The other main objective lies in identifying the strengths and weaknesses of each technique for the assessment of materials subjected to different strain-rate and temperature conditions

Preliminary analysing of experimental data for the development of high Cr Alloy Creep damage Constitutive Equations

This conference paper presents the current research of preliminary analysing of experimental data for the development of high Cr Alloy Creep damage Constitutive Equations (such as P91 alloy). Firstly, it briefly introduces the background of general creep deformation, rupture and continuum damage mechanics. Secondly, it illustrates the constitutive equations used for P91 alloy or its weldment, especially of the form and deficiencies of two kinds of most widely used typical creep damage constitutive equations Kachanov-Rabotnov-Hayhurst (KRH) and Xu’s formations. And then, the methodology for development of new set constitutive equation proposed by Xu (2004) has been followed in this research. Fourthly, there is a critically analysis of the specific experiment data for P91 alloy and its weldment. Afterwards, the specific requirements for developing a new set constitutive equation have been reported

New tension-compression damage model for complex analysis of concrete structures

A new damage model, based on continuum damage mechanics and simulating the opening, closing, and reopening of cracks in concrete using only one surface of discontinuity, is proposed in this article. The model complies with the thermodynamics principles of nonreversible, isothermal, and adiabatic processes. Two scalar internal variables have been defined: a tensile damage variable d+d+ and a compressive damage variable d-d-; the threshold of damage is controlled by only one surface of discontinuity and a new parameter controlling the damage variable that should be activated. This new parameter represents the ratio of tensile stress to compressive stress in the damaged material. The continuity of response under complex loads, which is one of the aims of this work, is ensured. An adequate response under different types of loads leads to the conclusion that the proposed model provides a powerful tool to numerically analyze reinforced concrete structures. Validation and illustrative examples are included in the article.Peer ReviewedPostprint (author's final draft

A differential CDM model for fatigue of unidirectional metal matrix composites

A multiaxial, isothermal, continuum damage mechanics (CDM) model for fatigue of a unidirectional metal matrix composite volume element is presented. The model is phenomenological, stress based, and assumes a single scalar internal damage variable, the evolution of which is anisotropic. The development of the fatigue damage model, (i.e., evolutionary law) is based on the definition of an initially transversely isotropic fatigue limit surface, a static fracture surface, and a normalized stress amplitude function. The anisotropy of these surfaces and function, and therefore the model, is defined through physically meaningful invariants reflecting the local stress and material orientation. This transversely isotropic model is shown, when taken to it's isotropic limit, to directly simplify to a previously developed and validated isotropic fatigue continuum damage model. Results of a nondimensional parametric study illustrate (1) the flexibility of the present formulation in attempting to characterize a class of composite materials, and (2) the capability of the formulation in predicting anticipated qualitative trends in the fatigue behavior of unidirectional metal matrix composites. Also, specific material parameters representing an initial characterization of the composite system SiC/Ti 15-3 and the matrix material (Ti 15-3) are reported