Inter-Element Crack Propagation with High-Order Stress Equilibrium Element

The present contribution proposes a formulation based on the use of hybrid equilibrium elements (HEEs), for the analysis of inter-element delamination and fracture propagation problems. HEEs are defined in terms of quadratic stress fields, which strongly verify both the homogeneous and inter-element equilibrium equations and they are employed with interfaces, initially exhibiting rigid behavior, embedded at the elements’ sides. The interface model is formulated in terms of the same degrees of freedom of the HEE, without any additional burden. The cohesive zone model (CZM) of the extrinsic interface is rigorously developed in the damage mechanics framework, with perfect adhesion at the pre-failure condition and with linear softening at the post-failure regime. After a brief review, the formulation is computationally tested by simulating the behavior of a double-cantilever-beam with diagonal loads; the obtained numerical results confirm the accuracy and potential of the method.

Modeling Brittle Fractures in Epoxy Nanocomposites Using Extended Finite Element and Cohesive Zone Surface Methods

Linear elastic fracture modeling coupled with empirical material tensile data result in good quantitative agreement with the experimental determination of mode I fracture for both brittle and toughened epoxy nanocomposites. The nanocomposites are comprised of diglycidyl ether of bisphenol A cured with Jeffamine D-230 and some were filled with core-shell rubber nanoparticles of varying concentrations. The quasi-static single-edge notched bending (SENB) test is modeled using both the surface-based cohesive zone (CZS) and extended finite element methods (XFEM) implemented in the Abaqus software. For each material considered, the critical load predicted by the simulated SENB test is used to calculate the mode I fracture toughness. Damage initiates in these models when nodes at the simulated crack tip attain the experimentally measured yield stress. Prediction of fracture processes using a generalized truncated linear traction–separation law (TSL) was significantly improved by considering the case of a linear softening function. There are no adjustable parameters in the XFEM model. The CZS model requires only optimization of the element displacement at the fracture parameter. Thus, these continuum methods describe these materials in mode I fracture with a minimum number of independent parameters.

Modeling Brittle Fracture in Epoxy Nanocomposites using Extended Finite Element and Cohesive Zone Surface Methods

Linear elastic fracture modeling coupled with empirical material tension data result in good quantitative agreement with experimental measurements of fracture failure for both brittle and tough epoxy nanocomposites. The nanocomposites comprise diglycidyl ethers of bisphenol A cured with O,O’ bis (2-aminopropylpropylene glycol) (Jeffamine D230) and doped with rubber nanoparticles of varying concentrations. Toughness, critical load, and critical displacement in quasi-static single edge-notched three-point bending are predicted accurately using both surface-based cohesive zone (CZS) and extended finite element (XFEM) methods implemented in Abaqus software. Fracture initiation within a crack is taken at the yield stress from uniaxial tension data. Prediction of fracture processes using a generalized truncated linear traction-separation law was significantly improved by considering the case of a linear softening function. There are no adjustable parameters in the XFEM model. The CZS model requires only optimization of the element displacement at fracture parameter. Thus, these continuum methods describe these materials in mode I fracture with a minimum number of independent parameters.

A Contribution to the Study of the Forming of Dry Unidirectional HiTape® Reinforcements for Primary Aircraft Structures

In the context of developing competitive liquid composites molding processes for primary aircraft structures, modeling the forming stage of automatically-placed initially flat stacks of dry reinforcements is of great interest. In the case of HiTape®, a dry unidirectional carbon fiber reinforcement designed to achieve performances comparable to state-of-the-art pre-impregnated materials, the presence of a thermoplastic veil on each side of the material for both processing and mechanical purposes should also be considered when modeling forming in hot conditions. As a dry unidirectional reinforcement, HiTape® is expected to exhibit a transversely isotropic behavior. Computation cost and strong characterization challenges led us to model its behavior at the forming process temperature (above the thermoplastic veil melting temperature) through a homogeneous equivalent continuous medium exhibiting four ‘classical’ deformation modes and a specific structural mode, namely out-of-plane bending. The response of both single plies and stacks of HiTape® to this latter structural mode was characterized at the forming process temperature using a modified Peirce flexometer. Results on single plies showed a non-linear softening moment-curvature behavior and a corresponding flexural stiffness much lower than what can be inferred from continuum mechanics. Moreover, testing stacks revealed that the veil acts as a thin load transfer layer between the plies undergoing relative in-plane displacement, i.e. inter-ply sliding. This inter-ply response was then characterized separately at the forming process temperature thanks to a specific method relying on a pull-through test. Experiments performed at pressures and speeds representative of the forming stage revealed that a hydrodynamic lubricated friction regime predominates, i.e. a linearly increasing relationship between the friction coefficient and the modified Hersey number. From an industrial point of view, high forming pressures and low speeds are therefore recommended to promote inter-ply slip to limit the occurrence of defects such as wrinkles.

Effect of the shape of the softening damage law on the predicted tensile fracturing and energy dissipation in textile composites

The fracturing behavior of fiber-reinforced composites is often modeled using continuum damage mechanics-based approaches which commonly assume a linear softening damage law, i.e. a linearly decreasing stress with increasing strain. The objective of this paper is to assess the suitability of this assumption for composites and to systematically analyze the effect of the assumed shape of the softening damage law at material point, on the predicted fracturing behavior of the structure. The material considered is an epoxy/carbon-fiber twill woven composite. Numerical evaluations are conducted by predicting the strength size effect and progressive accumulation of damage in a structure and comparing with experimental measurements. Damage models with a wide range of shapes of softening laws are considered. These include linear, bilinear, trilinear, exponential, power law and sigmoidal. The effect of introducing a sudden drop in the damage law is also evaluated. All modeling is conducted via the crack band model (CBM), to ensure the mesh objectivity of results. It is found that despite using the right strength and fracture energy as input at the material point level, not all softening law shapes can accurately predict the strength size effect and post-peak softening. Especially the sudden drop feature leads to severe underprediction of strength. Bilinear softening shows the best combination of simplicity and accuracy, especially if formulated via the R-curve approach. Further insights are obtained by assessing the predicted fracture process zone size and fracture energy via the size effect method. Finally structure level predictions are made by considering plug initiated axial crushing of a cylindrical crushcan. The close ties between the shape of the material softening law and predicted process zone, and structural fracturing are revealed, and shown to be an important consideration in formulating damage models.

Design and Development of a Constant Force Non-Linear Spring (CF-NLS) for Energy Storage

Development of constant force non-linear softening (CF-NLS) springs has recently gained attention in the literature due to their energy storage potential in many applications including robotics, biomechanics, machining, etc. These springs are typically designed by using computationally exhaustive topology optimization techniques which have shown to produce stress concentrations significantly reducing the operational life of the spring. Furthermore, current design methodologies including spline based optimizations are not exploiting the design space efficiently. There is a need of a computationally efficient design methodology capable of producing mechanisms without stress concentrations while more fully exploiting the design space. A new graph based design methodology is proposed by using a modified-depth first search (M-DFS) algorithm with 2D finite element analysis. A detailed parametric study is also conducted to design a mechanism by maximizing of the stored strain energy on a general stiffest-softening behavior. The proposed CF-NLS is validated experimentally and compared with mechanisms in the literature. It is observed that the proposed CF-NLS is providing more displacement capacity without stress concentrations and with less expensive materials due to improved exploitation of the design space. This proposed CF-NLS is beneficial for dynamic activities like walking, running and jumping robots or biomechanics where high energy storage capacity is required.

A Particle-Based Cohesive Crack Model for Brittle Fracture Problems

Numerical simulations of the fracture process are challenging, and the discrete element (DE) method is an effective means to model fracture problems. The DE model comprises the DE connective model and DE contact model, where the former is used for the representation of isotropic solids before cracks initiate, while the latter is employed to represent particulate materials after cracks propagate. In this paper, a DE particle-based cohesive crack model is developed to model the mixed-mode fracture process of brittle materials, aiming to simulate the material transition from a solid phase to a particulate phase. Because of the particle characteristics of the DE connective model, the cohesive crack model is constructed at inter-particle bonds in the connective stage of the model at a microscale. A potential formulation is adopted by the cohesive zone method, and a linear softening relation is employed by the traction–separation law upon fracture initiation. This particle-based cohesive crack model bridges the microscopic gap between the connective model and the contact model and, thus, is suitable to describe the material separation process from solids to particulates. The proposed model is validated by a number of standard fracture tests, and numerical results are found to be in good agreement with the analytical solutions. A notched concrete beam subjected to an impact loading is modeled, and the impact force obtained from the numerical modeling agrees better with the experimental result than that obtained from the finite element method.

Elastic-Plastic Analogy for Examination of Softening Response for Strip Yield Models

The manner in which the spread of inelastic deformation of a softening cohesive zone affects the load capacity is examined. The analysis makes use of an elastic-plastic analogy to the strip yield model applied to pure bending. The example of pure bending is one case where inelastic deformation contributes to enhancing the load capacity. The analytical solution to the elastic-plastic case is developed for zero hardening (baseline for strip yield case for which analytical solution is known) as well as for a range of linear softening rates. Evaluation of the results shows that the maximu m bending load capacity is always reached before the stress at the surface becomes zero.

Analysis of the Versatility of Multi-Linear Softening Functions Applied in the Simulation of Fracture Behaviour of Fibre-Reinforced Cementitious Materials

Fibre-reinforced cementitious materials (FRC) have become an attractive alternative for structural applications. Among such FRC, steel- and polyolefin fibre-reinforced concrete and glass fibre-reinforced concrete are the most used ones. However, in order to exploit the properties of such materials, structural designers need constitutive relations that accurately reproduce FRC fracture behaviour. This contribution analyses the suitability of multilinear softening functions combined with a cohesive crack approach for reproducing the fracture behaviour of the FRC mentioned earlier. The performed implementation accurately simulated fracture behaviour, while being versatile, robust, and efficient from a numerical point-of-view.

Analysis of the Versatility of Multi-linear Softening Functions Applied to the Simulation of the Fracture Behaviour of Fibre Reinforced Cementitious Materials

Fibre reinforced cementitious materials (FRC) have become an attractive alternative for structural applications. Among such FRC, steel and polyolefin fibre reinforced concrete and glass fibre reinforced concrete are the most used ones. However, in order to exploit the properties of such materials structural designers need constitutive relations that reproduce FRC fracture behaviour accurately. This contribution analyses the suitability of multilinear softening functions combined with a cohesive crack approach for reproducing the fracture behaviour of the FRC previously mentioned. The implementation performed accurately simulates the fracture behaviour while being versatile, robust and efficient from a numerical point of view.