Herzl Chai

One dimensional modelling of failure in laminated plates by delamination buckling

When low speed objects impact composite laminated plates delamination may result. Under inplane compression such delaminations may buckle and tend to enlarge the delaminated area which can lead to loss of global plate stability. This process is modelled here in a first attempt by a delaminating beam-column wherein the local delamination growth, stability and arrest are governed by a fracture mechanics-based energy release rate criterion.

Two-Dimensional Modelling of Compressive Failure in Delaminated Laminates

An analytical model is developed to assess the compressive strength criticality of near-surface interlaminar defects in laminated composites.

Remarkable resilience of teeth

Tooth enamel is inherently weak, with fracture toughness comparable with glass, yet it is remarkably resilient, surviving millions of functional contacts over a lifetime. We propose a microstructural mechanism of damage resistance, based on observations from ex situ loading of human and sea otter molars (teeth with strikingly similar structural features). Section views of the enamel implicate tufts, hypomineralized crack-like defects at the enamel–dentin junction, as primary fracture sources. We report a stabilization in the evolution of these defects, by “stress shielding” from neighbors, by inhibition of ensuing crack extension from prism interweaving (decussation), and by self-healing. These factors, coupled with the capacity of the tooth configuration to limit the generation of tensile stresses in largely compressive biting, explain how teeth may absorb considerable damage over time without catastrophic failure, an outcome with strong implications concerning the adaptation of animal species to diet.

Overview: Damage in brittle layer structures from concentrated loads

In this article, we review recent advances in the understanding and analysis of damage initiation and evolution in laminate structures with brittle outerlayers and compliant sublayers in concentrated loading. The relevance of such damage to lifetime-limiting failures of engineering and biomechanical layer systems is emphasized. We describe the results of contact studies on monolayer, bilayer, trilayer, and multilayer test specimens that enable simple elucidation of fundamental damage mechanics and yet simulate essential function in a wide range of practical structures. Damage processes are observed using post mortem (“bonded-interface”) sectioning and direct in situ viewing during loading. The observations reveal a competition between damage modes in the brittle outerlayers—cone cracks or quasiplasticity at the top (near-contact) surfaces and laterally extending radial cracks at the lower surfaces. In metal or polymeric support layers, yield or viscoelasticity can become limiting factors. Analytical relations for the critical loads to initiate each damage mode are presented in terms of key system variables: geometrical (layer thickness and indenter radius); material (elastic modulus, strength and toughness of brittle components, hardness of deformable components). Such relations provide a sound physical basis for the design of brittle layer systems with optimal damage thresholds. Other elements of the damage process—damage evolution to failure, crack kinetics (and fatigue), flaw statistics, and complex (tangential) loading—are also considered.

On the correlation between the mode I failure of adhesive joints and laminated composites

Abstract The effect of the matrix constituent on the Mode I interlaminar fracture of laminated composites was determined directly by comparing test results obtained from composite and adhesive joint specimens fabricated from identical matrices. Resins of diverse mechanical properties were employed, including brittle and thermoplastic (PEEK) types. The brittle adhesives exhibited essentially no bond thickness ( t ) effect but the fracture conditions of PEEK heavily depended on t . At bond thicknesses approximating the interlaminar resin layer the adhesive fracture energy of PEEK decreased with bond thickness. This interesting behavior that was observed also for BP-907 [H. Chai, 7th ASTM Symp. on Composite Materials, Testing and Design, 2–4 April 1984], a toughened resin, was attributed to the development of a state of nearly “hydrostatic” tension over the majority of the adhesive layer at the crack tip vicinity. In fact, scanning electron micrographs of the fractured surfaces revealed that failure actually occurred by means of shear-yielding that originated from the vicinity of the metal-matrix interface. The brittle (AS4/3502) and ductile (APC-2) matrix-based composites tested exhibited a “resistance” type fracture curve that helped to explain the large variance or scatter in G IC values reported in the literature for a given composite. Only over the initial phase of the crack growth was the failure truly interlaminar and the fracture energy independent of specimen geometry. This value was considered, therefore, as the true measure of G IC . The composite toughness, thus defined, fully coincided with its respective adhesive toughness, provided the thickness of the adhesive layer was sufficiently small.

Observation of damage growth in compressively loaded laminates

An experimental program to determine the phenomenological aspects of composite-panel failure under simultaneous compressive in-plane loading and low-velocity transverse impact [0-75 m/s (0-250 ft/s)] is described. High-speed photography coupled with the shadow-moiré technique is used to record the phenomenon of failure propagation. The information gained from these records, supplemented by plate sectioning and observation for interior damage, has provided information regarding the failure-propagation mechanism.The results show that the failure process can be divided roughly into two phases. In the first phase the plate is impacted, and the resulting response causes interlaminar separation. In the second phase the local damage spreads to the undamaged portion of the plate through a combination of laminae buckling and further delamination.

Tooth chipping can reveal the diet and bite forces of fossil hominins

Mammalian tooth enamel is often chipped, providing clear evidence for localized contacts with large hard food objects. Here, we apply a simple fracture equation to estimate peak bite forces directly from chip size. Many fossil hominins exhibit antemortem chips on their posterior teeth, indicating their use of high bite forces. The inference that these species must have consumed large hard foods such as seeds is supported by the occurrence of similar chips among known modern-day seed predators such as orangutans and peccaries. The existence of tooth chip signatures also provides a way of identifying the consumption of rarely eaten foods that dental microwear and isotopic analysis are unlikely to detect.

Three-dimensional fracture analysis of thin-film debonding

A simplified mixed-mode fracture analysis combining nonlinear thin-plate stress solutions with crack-tip elasticity results has been developed to account for local variations of GI, GII and GIII in thin-film debond problems associated with large film deformations. Membrane and bending stresses from the plate analysis are matched with the crack-tip singularity solution over a small boundary region at the crack tip where the effect of geometric nonlinearity is small. Local variations in each of the individual components of the energy release rate are directly related to the “jump” in these stresses across the crack border.Specific results are presented for 1-D and elliptical planeform cracks. Deformations were induced either by a pressure acting normal to the film surface or biaxial compression or tension stresses applied to the substrate in which the loading axes and debond axes coincide. The latter type of loading involves buckling of the delaminated film. The model predictions compare well with more rigorous solutions provided the film thickness is small compared to the debond dimensions. In all cases analyzed, GIII was negligible. The ratio GI/GII typically decreases with increasing load or film deformation, the rate was moderate for pressure loading while generally sharp for compression loading. Film-substrate overlap may occur for certain debond geometry and loading conditions. Prevention of this by the substrate may critically increase the energy available for crack propagation.

Fracture Modes in Human Teeth

The structural integrity of teeth under stress is vital to functional longevity. We tested the hypothesis that this integrity is limited by fracture of the enamel. Experiments were conducted on molar teeth, with a metal rod loaded onto individual cusps. Fracture during testing was tracked with a video camera. Two longitudinal modes of cracking were observed: median cracking from the contact zone, and margin cracking along side walls. Median cracks initiated from plastic damage at the contact site, at first growing slowly and then accelerating to the tooth margin. Margin cracks appeared to originate from the cemento-enamel junction, and traversed the tooth wall adjacent to the loaded cusp from the gingival to the occlusal surface. All cracks remained confined within the enamel shell up to about 550 N. At higher loads, additional crack modes—such as enamel chipping and delamination—began to manifest themselves, leading to more comprehensive failure of the tooth structure.

THE POST-BUCKLING RESPONSE OF A BI-LATERALLY CONSTRAINED COLUMN

Abstract The post-buckling behavior of a linearly elastic column under a bi-lateral constraint is studied experimentally and analytically with an eye toward applications to corrugated sandwich structures. Under a controlled axial displacement, a rather rich sequence of events unfolds, including the formation of discrete or continuous contact zones between the column and the guiding walls and the instantaneous transition of the buckling waveform to a new equilibrium configuration due to local instability. The specific details, which depend on the system parameters as well as on the loading direction, are quantified based on the linearized differential equation of the column and without recourse to imperfections or energy considerations. For a frictionless contact, the response of the column exhibits a degree of statistical variation, but the range of this variation can be bounded. A companion elastica type analysis is also developed to account for large rotations which occur at large end shortenings. Under this condition, the ever repeating mode transition process which is predicted by the small deformation analysis ceases. Other interesting buckling characteristics are found which should be useful for the understanding of more complex contact/stability systems.