Organised by ESIS TC8 “Numerical Methods”
Tuesday, 07 July 2020
Models for ductile fracture
Ductile fracture encompasses several failure modes observed in metal alloys where, broadly speaking, large irreversible strains are involved at some scale. After reviewing experimental observations of these failure modes, models used for ductile fracture through void growth to coalescence are reviewed. In a first part, key features of the mechanical behavior of porous materials are described based on experimental results and porous unit cells simulation results. In a second part, the basic homogenized models for porous isotropic materials widely used in ductile fracture modelling – Gurson and Thomason models – are derived. The strengths and weaknesses of these models are detailed, and some of the extensions proposed in the literature are discussed and compared. In a third part, some recent ductile fracture models accounting for crystal plasticity or inhomogeneous yielding are presented.
Models for brittle fracture
The ability to predict cleavage fracture toughness changes due to temperature and geometry effects is critical to safety assessment and life extension decisions of infrastructure and plants. Global approaches to integrity assessment, such as those based on the failure assessment diagram, are overly conservative without explicit knowledge of fracture toughness values for every particular material state and crack geometry, i.e. without extensive testing, which is not feasible in all cases. Local approaches to cleavage fracture are considered to be a promising mechanistic alternative to global approaches for failure assessments. These have been developed over the last 30 years with the view to incorporate microstructure information and mechanisms, including the effects of plasticity and stress triaxiality. The lecture will offer a review of this development, which will demonstrate where the current state-of-the-art in local approaches to cleavage can be successfully applied and where challenges remain. Specifically, it will be shown that the transferability question is yet to be fully addressed, i.e. using parameters calibrated with experimental data from one crack geometry to calculate the apparent toughness of another crack geometry is still problematic. Potential avenues for addressing this critical issue will also be discussed. It is anticipated that presenting the mathematical basis and the remaining challenges will be motivating for the next generation of researchers in this important area.
Non local models for fracture
Conventionally, structures and components have been designed by criteria for admissible levels of stress or strain. However, ductile materials offer a safety reserve of plastic deformations not only during global plastification, but even after initiation of a crack. The reliable simulation of ductile damage behavior and crack propagation is not only required for accident scenarios, but allows for more efficient material usage. Fracture mechanics concepts are suitable to assess the crack propagation stage, but are unable to predict the formation of cracks during global plastic deformations. Damage mechanics can overcome this problem by implementing the local material degradation directly into the constitutive model of the material by means of evolving internal state variables. In particular, the models of Gurson, Rousselier or effective-stress type models, and numerous modifications thereof, have been used successfully to simulate the ductile damage mechanism. However, finite element simulations with these models turned out to exhibit a pathological mesh sensitivity in the softening regime. The reason is that these models are formulated within the conventional framework of so-called simple materials and do not possess an intrinsic length scale. Declaring the element size as an intrinsic length is a pragmatic approach which comes to its limits if the crack path is not known in advance or if different element types need to be used.
More recent approaches embed the intrinsic length directly into the continuum mechanics model and can thus overcome the pathological mesh sensitivity. Different techniques and approaches of this type have been proposed and evaluated during the last 25 years, like strongly nonlocal models, gradient-enhanced, phase-field or micromorphic models.
The lecture gives an overview over these techniques with a special focus on finite-element simulations of ductile damage and crack propagation.
Dynamic fracture in solids has attracted much attention for several decades for its technological implications and fundamental scientific interest. Rapidly applied loads are encountered in several technical applications such as blasting, mining, ballistic impacts, etc. To define suitable design routes to assess the susceptibility to fracture, the knowledge of the mechanisms controlling the deformation and fracture of materials at high strain rates, is necessary. In this lecture, the mechanisms of fracture occurring in metals and alloys at high strain rates are reviewed, followed by a brief survey of the experimental methods used for generating dynamic loading. Then, a presentation of constitutive/failure models is given. Finally, some practical examples of modelling and simulation of dynamic fracture in solids at different length scales are presented.