J.A.W. van Dommelen

The relation between single crystal elasticity and the effective elastic behaviour of polycrystalline materials: theory, measurement and computation

Due to continuing miniaturization, characteristic dimensions of electronic components are now becoming of the same order of magnitude as the characteristic microstructural scales of the constituent materials, such as grain sizes. In this situation, it is necessary to take into account the influence of microstructure when studying the mechanical behaviour. In this paper, we focus on the relation between the (anisotropic) properties of individual grains and the effective elastic behaviour of polycrystalline materials. For large volumes of materials, the conventional averaging theory may be applied. This is illustrated with experiments on various barium titanates. For small volumes of material, we examine the relationship by means of micromechanical computations using a finite-element model, allowing the simulation of a real microstructure, based on a microscopic image of the grain structure. Various cubic and tetragonal materials are studied. The computational results clearly show the influence of the specific microstructural properties on the effective elastic behaviour.

Micromechanics of diffuse axonal injury : influence of axonal orientation and anisotropy

Multiple length scales are involved in the development of traumatic brain injury, where the global mechanics of the head level are responsible for local physiological impairment of brain cells. In this study, a relation between the mechanical state at the tissue level and the cellular level is established. A model has been developed that is based on pathological observations of local axonal injury. The model contains axons surrounding an obstacle (e.g., a blood vessel or a brain soma). The axons, which are described by an anisotropic fiber-reinforced material model, have several physically different orientations. The results of the simulations reveal axonal strains being higher than the applied maximum principal tissue strain. For anisotropic brain tissue with a relatively stiff inclusion, the relative logarithmic strain increase is above 60%. Furthermore, it is concluded that individual axons oriented away from the main axonal direction at a specific site can be subjected to even higher axonal strains in a stress-driven process, e.g., invoked by inertial forces in the brain. These axons can have a logarithmic strain of about 2.5 times the maximum logarithmic strain of the axons in the main axonal direction over the complete range of loading directions. The results indicate that cellular level heterogeneities have an important influence on the axonal strain, leading to an orientation and location-dependent sensitivity of the tissue to mechanical loads. Therefore, these effects should be accounted for in injury assessments relying on finite element head models.

The influence of anisotropy on brain injury prediction

Traumatic Brain Injury (TBI) occurs when a mechanical insult produces damage to the brain and disrupts its normal function. Numerical head models are often used as tools to analyze TBIs and to measure injury based on mechanical parameters. However, the reliability of such models depends on the incorporation of an appropriate level of structural detail and accurate representation of the material behavior. Since recent studies have shown that several brain regions are characterized by a marked anisotropy, constitutive equations should account for the orientation-dependence within the brain. Nevertheless, in most of the current models brain tissue is considered as completely isotropic. To study the influence of the anisotropy on the mechanical response of the brain, a head model that incorporates the orientation of neural fibers is used and compared with a fully isotropic model. A simulation of a concussive impact based on a sport accident illustrates that significantly lowered strains in the axonal direction as well as increased maximum principal strains are detected for anisotropic regions of the brain. Thus, the orientation-dependence strongly affects the response of the brain tissue. When anisotropy of the whole brain is taken into account, deformation spreads out and white matter is particularly affected. The introduction of local axonal orientations and fiber distribution into the material model is crucial to reliably address the strains occurring during an impact and should be considered in numerical head models for potentially more accurate predictions of brain injury.

An improved miniature mixed-mode delamination setup for in-situ microscopic interface failure analyses

Precise characterization of interface delamination in miniature interface structures is an ongoing challenge with the advent of miniaturization and multi-functionality in the electronics industry. Accurate numerical prediction of the interface behaviour is necessary to minimize delamination failures. Successful prediction requires (i) accurate determination of the interface properties like the critical energy release rate (CERR) over the full range of mode mixities and (ii) simultaneous in situ microscopic visualization of the delamination mechanism. These requirements were recently addressed by the development of the miniature mixed-mode bending (MMMB) setup (Kolluri et al 2009 Int. J. Fract.). In this paper an improved MMMB setup is presented, which overcomes the main limitations of the original design. Specifically, the improved design (i) can access a significantly larger range of interface systems due to its increased limits of maximum accessible load and stroke in all mode mixities, (ii) has significantly higher accuracy in load–displacement measurement due to its reduced clearance at the connectors, which is particularly relevant for miniature samples, and (iii) has a high reproducibility due to a newly added setup alignment tool. The measurement concept is validated on (industrially relevant) copper lead frame–moulding compound epoxy interface structures. The load–displacement curves and corresponding CERR values obtained from experiments over the full range of mode mixities are discussed in relation to the delamination mechanism observed during real-time in situ visualization. Specifically, the measured increase in the CERR towards mode II is related to a more discrete or jerky crack growth behaviour observed in the mode II dominant tests. Finally, the potential of the methodology for interface parameter characterization is illustrated.

Irreversible mixed mode interface delamination using a combined damage-plasticity cohesive zone enabling unloading

Delamination is often identified as an important failure mechanism in structures with a high interface density, such as modern microelectronic systems and advanced composite materials. Delamination tests performed on different interface structures reveal complex failure mechanisms (crack bridging, fibre pull out, micro-void coalescence, fibrilation, crack meandering, etc.) in the fracture process zone that lead to an irreversible unloading response of the interface, ranging from full damage to full plasticity. Modeling the unloading response of an interface is important for predicting phenomena such as crack branching and crack propagation at multiple interfaces. This paper presents a 2D irreversible combined plasticity-damage unloading model, which can be used to extend the cohesive zone (loading) models with a proper unloading description that is suitable for modeling the entire loading-unloading response in the process zone. The presented model is able to capture changes in unloading behavior as a function of mode mixity, whereas it introduced only two additional model parameters that can be determined from dedicated delamination experiments. As a demonstration, the improved Xu–Needleman cohesive zone law has been extended with the proposed combined damage-plasticity unloading formulation. Numerical simulations with this extended model are performed for a glue interface system, recovering the typical observed behavior in delamination experiments. Finally, a complete procedure to extract all CZ model parameters is presented and illustrated for the glue interface system.

A practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment

Interfacial delamination is a key reliability challenge in composites and micro-electronic systems due to (high density) integration of dissimilar materials. Predictive finite element models require the input of interface properties, often determined with an interface delamination growth experiment with (nearly) constant process zone, relying on the assumption of no permanent deformation in the sample structure layers. However, much evidence in the literature exists that plasticity often does occur in the sample structure during delamination experiments, which should be adequately dealt with to obtain the real interface fracture toughness that is independent of the thickness of the two sample arms. This paper presents a practical approach for the separation of interfacial toughness and structural plasticity in a delamination growth experiment on a double-cantilever beam specimen involving only small-scale plasticity at the interface. The procedure does not require knowledge of the constitutive behavior of the adherent layers. It only deals with the separation of structural plasticity in the adherents, whereas small-scale plasticity in connection with ductile interface fracture is lumped into the interface fracture toughness. The proposed approach was numerically verified for one set of parameters. Experimental assessment of the approach on industrially-relevant copper lead frame–molding compound epoxy interface structures showed a correction of the interface fracture toughness of more than a factor of two, demonstrating the potentially significant errors induced by plastic deformation of the sample structure during delamination experiments.

An enriched cohesive zone model for numerical simulation of interfacial delamination in microsystems

Interfacial failure, mainly in the form of debonding or delamination of brittle interfaces, is one of the major sources of failure in microsystems that consist of multiple thin and stacked layers, manufactured using different materials. A cohesive zone model with a simple traction- separation law is employed to simulate the benchmark test of pure mode I delamination in a double cantilever beam. A local arc-length control procedure is also detailed and its robustness is shown in the case that the quasi-static solution contains limit points due to the brittle nature of the interface considered here. Finally, a bilinear hierarchical extension is proposed to enhance the efficiency and robustness of cohesive zone models by enriching the separation approximation in the process zone of a cohesive crack in brittle interfaces without need for further mesh refinement.

Advanced miniature mixed mode bending setup for in-situ interface delamination characterization

A novel test frame configuration was developed and employed to design a new miniature mixed mode bending (MMMB) setup for in-situ characterization of interface delamination in miniature multi-layer structures to accomplish full range of mode mixities. This advanced setup is specially designed with sufficiently small dimensions to fit in a scanning electron microscope and under an optical microscope for detailed real-time fracture analysis during delamination. Analysis of the loads in the new test configuration was performed and a special loading configuration was identified which replicates pure mode II loading better than the conventional end notch flexture (ENF) test. Special care was taken to minimize non-linearities, such as friction, the influence of gravity and geometrical non-linearities. Finite element simulation of the designed setup were performed to show its ability to access all loading modes. Preliminary delamination tests conducted on homogeneous bilayer samples under scanning electron microscope (SEM) proved the new setup configuration is capable of measuring the crack length, crack opening profile and crack delamination mechanism in addition to the conventional energy release rate measurements.

Mechanics of amorphous solids—identification and constitutive modelling

Both polymers and metals can be in an organised crystalline or amorphous glassy state, where for polymers usually at least a part of the structure is amorphous and metals are in a glassy state only when processed under special conditions. At the 15th European Mechanics of Materials Conference in September 2016 in Brussels, Belgium, a session focussing on the mechanical properties of amorphous or partly amorphous solid materials was organised, attempting to bridge descriptions found for metallic glasses and polymers, which share some common features, such as a rate- and temperature-dependent response, being prone to strain localisation in the form of shear bands, the occurrence of damage by cavitation, etc.