An interface element based on the partition of unity

An alternative interface finite element is developed. By using the partition of unity property of finite element shape functions, discontinuous shape functions are added to the standard finite element basis. The interface behaviour is described by extra degrees of freedom at existing nodes, avoiding the need for ‘doubled nodes’. The element is kinematically equivalent to a conventional interface element but is more flexible because it allows the inclusion of interface surfaces within solid elements. In describing interface phenomena, the methodology proposed here makes possible the use of coarser meshes and it is completely insensitive to mesh topology. The new formulation is analysed throughly and comparisons are drawn with the conventional formulation

Analysis of delamination growth with discontinuous finite elements

In this contribution a new finite element is presented for the simulation of delamination growth in thin layered composite materials. The element is based on the solid-like shell element, a volume element that can be used in very thin applications due to a higher order displacement field in thickness direction. The delamination crack is incorporated in this element as a jump of the displacement field by means of the partition of unity method. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples

Analysis of delamination growth with discontinuous solid-like shell elements

Delamination is one of the most important failure mechanisms in laminates. Normally, it is modelled using interface elements. These elements are placed between two layers that are modelled with continuum elements. The interface elements are equipped with a softening or damage model in order to simulate debonding. This method has some drawbacks, both in a numerical and in a mechanical sense. A recent alternative is to simulate the crack by adding a discontinuous displacement mode to the continuum elements according to the partition of unity method. The elements do not contain the discontinuity prior to cracking, but when the ultimate stress in the bulk material is exceeded, delamination is initiated and additional degrees-of-freedom are activated. Beside this, a slightly different implementation is examined also. A discontinuity is predefined and has an initial dummy stiffness. Delamination is initiated when the tractions in the discontinuity exceed a threshold value. The results of both versions of this partition of unity model are compared mutually and with conventional interface elements by means of two examples

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

© 2017, The Author(s). Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations

A discrete dislocation analysis of hydrogen-assisted mode-I fracture

© 2016 Elsevier LtdFracture of engineering alloys in the presence of hydrogen commonly occurs by decohesion along grain boundaries via a mechanism known as hydrogen induced decohesion (HID). This mechanism is investigated here by analysing the mode-I fracture of a single crystal with plastic flow in the crystal described by discrete dislocation plasticity (DDP) and material separation (decohesion) modelled using a cohesive zone formulation. The motion of dislocations is assumed to be unaffected by hydrogen diffusion. While the cohesive strength is assumed to be reduced proportional to the local hydrogen concentration. Two limiting cases are analysed: (i) the fast diffusion limit where the hydrogen within the material is assumed to be at chemical equilibrium throughout the loading so that there is a high hydrogen concentration in the regions of high hydrostatic stress around dislocations and near the crack tip and (ii) the slow diffusion limit where we assume that there is no appreciable hydrogen diffusion over the duration of loading and thus the hydrogen concentration remains spatially uniform as in a stress-free material. The lower cohesive strength at high hydrogen concentrations results in reduced dislocation activity around the crack tip and a reduction in the material toughness. In fact, at the highest hydrogen concentrations analysed here, crack growth primarily occurs in an elastic manner. However, surprisingly the calculations predicted that the toughness in the fast diffusion case was no more than 12% lower compared to the slow diffusion case suggesting that the stress concentrations due to the dislocation structures and the crack tip fields have only a minor effect on the toughness reduction in the presence of hydrogen. The DDP calculations are finally used to investigate the sensitivity of the material toughness to the grain boundary cohesive strength. The calculations show that the toughness of materials with a small cohesive opening at the peak cohesive traction are more sensitive to hydrogen loading. We speculate that this result might be used as a guide in grain boundary engineering to design alloys that are less sensitive to hydrogen embrittlement by the HID mechanism

Shear response of 3D non-woven carbon fibre reinforced composites

We experimentally and numerically investigated the shear response of a three-dimensional (3D) non-woven carbon fibre reinforced epoxy composite with three sets of orthogonal tows and approximately equal fibre volume fractions in the orthogonal directions. Shear tests on two orientations of dogbone specimens showed significant strain hardening and an increasing unloading stiffnesses with increasing applied strain. Unloading was also accompanied by considerable strain recovery, with X-ray tomographic scans revealing minimal damage accumulation in specimens until near final failure at shear strains in excess of 50%. To understand the origins of this unusual mechanical response of the 3D carbon fibre composites, we developed a micro-mechanical model wherein all tows and matrix pockets in the composite are explicitly considered. The tows were modelled using a pressure-dependent crystal plasticity approach to capture texture evolution under large deformations and the model replicated many of the experimental observations with a high degree of fidelity. Importantly, the model illustrated the role of the 3D architecture in not only suppressing delamination but also enhancing the strain hardening response due to a 3D confinement effect of the tow architecture. On the other hand, a model wherein the tows were modelled using an anisotropic Hill plasticity framework (absent plastic spin) failed to replicate the observed strain hardening response or capture the associated strain recovery upon unloading. This highlights the importance of accounting for the evolution of the material substructure within the tows of these high ductility 3D composites. The results of this work illustrate the unique mechanical behaviour of 3D nonwoven fibre composites and provide insight into how 3D fibre architecture can be used to enhance the mechanical performance of fibre composites.Office of Naval Researc

The cohesive band model: A cohesive surface formulation with stress triaxiality

In the cohesive surface model cohesive tractions are transmitted across a two-dimensional surface, which is embedded in a three-dimensional continuum. The relevant kinematic quantities are the local crack opening displacement and the crack sliding displacement, but there is no kinematic quantity that represents the stretching of the fracture plane. As a consequence, in-plane stresses are absent, and fracture phenomena as splitting cracks in concrete and masonry, or crazing in polymers, which are governed by stress triaxiality, cannot be represented properly. In this paper we extend the cohesive surface model to include in-plane kinematic quantities. Since the full strain tensor is now available, a three-dimensional stress state can be computed in a straightforward manner. The cohesive band model is regarded as a subgrid scale fracture model, which has a small, yet finite thickness at the subgrid scale, but can be considered as having a zero thickness in the discretisation method that is used at the macroscopic scale. The standard cohesive surface formulation is obtained when the cohesive band width goes to zero. In principle, any discretisation method that can capture a discontinuity can be used, but partition-of-unity based finite element methods and isogeometric finite element analysis seem to have an advantage since they can naturally incorporate the continuum mechanics. When using interface finite elements, traction oscillations that can occur prior to the opening of a cohesive crack, persist for the cohesive band model. Example calculations show that Poisson contraction influences the results, since there is a coupling between the crack opening and the in-plane normal strain in the cohesive band. This coupling holds promise for capturing a variety of fracture phenomena, such as delamination buckling and splitting cracks, that are difficult, if not impossible, to describe within a conventional cohesive surface model. © 2013 Springer Science+Business Media Dordrecht

Finite versus small strain discrete dislocation analysis of cantilever bending of single crystals

© 2017, The Author(s). Plastic size effects in single crystals are investigated by using finite strain and small strain discrete dislocation plasticity to analyse the response of cantilever beam specimens. Crystals with both one and two active slip systems are analysed, as well as specimens with different beam aspect ratios. Over the range of specimen sizes analysed here, the bending stress versus applied tip displacement response has a strong hardening plastic component. This hardening rate increases with decreasing specimen size. The hardening rates are slightly lower when the finite strain discrete dislocation plasticity (DDP) formulation is employed as curving of the slip planes is accounted for in the finite strain formulation. This relaxes the back-stresses in the dislocation pile-ups and thereby reduces the hardening rate. Our calculations show that in line with the pure bending case, the bending stress in cantilever bending displays a plastic size dependence. However, unlike pure bending, the bending flow strength of the larger aspect ratio cantilever beams is appreciably smaller. This is attributed to the fact that for the same applied bending stress, longer beams have lower shear forces acting upon them and this results in a lower density of statistically stored dislocations

Computational Analysis of Crack Deflection at a Bi-Material Interface by means of Initially Rigid and Elastic Mixed-mode Traction-Separation Laws.

Numerical analyses of interfaces in layered samples are commonly performed with cohesive zone models, for which several types of traction-separation laws have been proposed. Most laws are initially elastic, which may result in an undesired compliance of the material when modeling bulk fracture. To overcome this problem, this study presents an exponential initially rigid tractionseparation law.\u3cbr/\u3eThe initially rigid model is compared to an initially elastic model for various loading conditions. It is shown that the proposed model is capable of describing both single mode and mixed-mode behavior, and correctly determines the work-of-separation. A dissipation-based arc-length solver, compatible with both models, is implemented to account for snap-backs in the load-displacement\u3cbr/\u3ecurve.\u3cbr/\u3eThe competition between bulk fracture and delamination in a bi-material sample is analyzed, in which the substrate is modeled with subsequently initially rigid and initially elastic models. The results are in agreement with an LEFM solution for substrate fracture, but the assumption of pure shear opening of the interface results in an overprediction of the required load for delamination. Both models predict similar substrate-to-interface strength and toughness ratios at which transition between the failure modes occurs and an increased load is observed for equal fracture length scales of the substrate and interface