Carl-Ernst Rousseau

A functionally graded particulate composite: Preparation, measurements and failure analysis

Abstract A functionally graded composite is prepared and the spatial gradation of Youngs modulus in the functionally graded material (FGM) is measured. Elastic modulus gradients occur over length scales suitable for experimental mechanics investigations using optical interferometry. Crack tip fields are mapped in the FGM under quasi-static loading conditions with cracks oriented perpendicular to the direction of the elastic gradient and near the interface of the graded and the homogeneous portions of three-point-bending specimens. The optical measurements are used to extract fracture parameters based on the prevailing understanding of the crack tip behavior in FGMs. The results are also compared with finite element computations which incorporate measured elastic properties of the FGM. The advantage of using FGM interlayer as opposed to piecewise homogeneous joints is demonstrated through crack initiation tests.

Compositionally graded materials with cracks normal to the elastic gradient

Mixed-mode crack tip deformations and fracture parameters in glass-filled epoxy beams with cracks normal to the elastic gradient are studied. Crack tip fields are optically measured for different crack locations in the elastic gradient when subjected to symmetric pure bending. A companion finite element model is developed and validated by the measurements. The numerical model is then used to examine the influence of the elastic gradient on crack location by evaluating stress intensity factor, mode-mixity and energy release rate. For certain crack locations, computed stress intensity factors and energy release rates in the graded material exceed that of the bimaterial counterpart. However, when reconciled with measured critical values of the fracture parameters, graded beams show consistently better performance for all crack locations in the graded region. Crack kinking due to compositional gradients are examined and are successfully compared with the vanishing KII criterion based on a locally homogeneous material behavior.

Dynamic fracture of compositionally graded materials with cracks along the elastic gradient: experiments and analysis

Abstract Crack tip deformation and fracture parameter histories in compositionally graded glass-filled epoxy are evaluated for low velocity impact loading. The situations when the elastic gradient is unidirectional with crack orientation along the gradient are examined. The fracture behavior of graded compositions is studied relative to homogeneous counterparts made of identical constituents. Optical method of CGS and high-speed photography are used to measure crack tip deformations prior to crack initiation and during dynamic crack growth. The apparent stress intensity factors prior to crack initiation are determined using dynamic equivalent of the stationary fields for FGMs while crack tip fields for steadily growing cracks in FGMs are used for post-initiation situations. Results from finite element simulations up to crack initiation are in excellent agreement with the experimental evaluations. Post crack initiation stress intensity factor histories and crack growth resistance behaviors for FGMs with monotonically increasing and decreasing elastic gradient are strikingly different. When the crack growth occurs into material with progressively increasing filler volume fraction, continuously increasing KID(t) is seen while a decreasing trend is observed when the gradient is of the opposite sense. The fracture behaviors are explained by independent fracture tests and fractured surface micrographs.

Influence of elastic gradient profiles on dynamically loaded functionally graded materials: cracks along the gradient

The effect of different elastic gradient profiles on the fracture behavior of dynamically loaded functionally graded materials (FGM) having cracks parallel to the elastic gradient is studied numerically. Finite element analyses of FGM and homogeneous beams are used to examine crack tip responses to low velocity, symmetric impact loading on the uncracked edge of the beams. Elastic description of FGMs consist of unidirectional power-law variation of E/ρ and constant Poissons ratio. The results show the effect of the variations in elastic profiles to be relatively small for cases with cracks residing on the stiff side of the FGM whereas significant differences are seen when cracks are on the compliant side. Elastic property variations also affect crack tip loading rate and hence crack initiation in FGMs. Crack initiation in FGMs with cracks on the stiff side are significantly delayed due to a lower rate of crack tip loading when compared to the opposite configuration or the equivalent homogeneous materials.

Evaluation of crack tip fields and stress intensity factors in functionally graded elastic materials: Cracks parallel to elastic gradient

Particulate functionally graded materials (FGM) made of glass-filled epoxy with edge cracks parallel to the direction of the elastic gradient and subjected to pure bending have been studied. Crack tip measurements are used to examine continuum models for FGMs by treating the material as isotropic and nonhomogeneous at macroscales. Situations where cracks are located on the compliant and the stiff sides of the beams are separately examined by mapping crack tip deformations using optical interferometry. Comparative experiments on homogeneous compositions corresponding to identical elastic properties of the crack tip region in the FGM are also undertaken. A methodology for extracting fracture parameters in FGMs based on locally homogeneous material descriptions is advanced. Companion finite element models are used to aid the development of fringe analysis procedures and to provide a direct comparison to the optical measurements. Stress intensity factors in FGMs are compared to each other and to their homogeneous counterparts. Optical measurements near quasi-statically growing cracks in FGMs have been undertaken, and crack growth resistance behavior is explained using crack initiation toughness variation as a function of filler volume fraction in homogeneous sheets.

On the influence of fault bends on the growth of sub‐Rayleigh and intersonic dynamic shear ruptures

Earthquake ruptures are modeled as dynamically propagating shear cracks with the aim of gaining insight into the physical mechanisms governing their arrest or, otherwise, the often-observed variations in rupture speeds. Fault bends have been proposed as being the main cause for these variations. Following this line of reasoning, the existence of deviations from fault planarity is chosen as the main focus of this study. Asymmetric impact is used to generate shear loading and to propagate dynamic mode-II cracks along the bonded interfaces of two otherwise identical homogeneous constituents. Secondary paths inclined at various angles are also introduced to represent fault bends or kinks. The experiments show that certain fault bend inclinations are favored as alternate paths for rupture continuation, whereas others suppress further motion of the incoming rupture. The asymptotic elastodynamic stress fields at the tip of the growing rupture are used to develop two criteria (one energetic and one stress based) for rupture propagation or arrest at the kinked interfaces. These criteria correlate very well with the experimental results. Since most field evidence suggests that the average rupture speeds during crustal earthquakes are sub-Rayleigh, this work first focuses on incoming rupture speeds that are just below the Rayleigh wave speed. Reports of intersonic crustal fault rupture speeds having surfaced recently, experiments and analyses are also performed within that speed regime.

Influence of elastic variations on crack initiation in functionally graded glass-filled epoxy

Crack tip deformations and fracture parameters in functionally graded glass-filled epoxy beams are experimentally evaluated under static and dynamic loading conditions. Beams with unidirectional, monotonic elastic gradients and cracks along the gradient are examined. SEN samples with increasing or decreasing Youngs modulus ahead of the crack tip are studied in symmetric four-point bending and one-point impact loading configurations. Optical method of coherent gradient sensing (CGS) is used to measure crack tip deformations prior to crack initiation. For impact loading experiments, CGS is used in conjunction with high-speed photography for recording instantaneous deformation fields. Stress intensity factors (SIF) or SIF-histories in functionally graded materials (FGM) based on locally homogeneous material descriptions in the immediate crack tip vicinity are evaluated and compared with companion finite element simulations. The influence of elastic gradients in FGM samples with cracks on the compliant and stiff sides of the beam are quantified relative to their homogeneous counterparts and with each other. Under static loading conditions, the crack tip located on the compliant side of the beam is elastically shielded when compared to the situation when the crack is on the stiffer side of the same FGM beam. Under dynamic conditions, however, elastic gradients affect crack initiation differently. Crack initiation in an FGM with a crack on the stiff side of the beam and impact occurring on the compliant edge is delayed when compared to the opposite configuration. Independent finite element simulations of FGMs with idealized elastic gradients with identical crack tip elastic properties suggest that lower crack tip loading rate in the former is responsible for the differences.

Finite element simulations of dynamic shear rupture experiments and dynamic path selection along kinked and branched faults

We analyze the nucleation and propagation of shear cracks along nonplanar, kinked, and branched fault paths corresponding to the configurations used in recent laboratory fracture studies by Rousseau and Rosakis (2003, 2009). The aim is to reproduce numerically those shear rupture experiments and from that provide an insight into processes which are active when a crack, initially propagating in mode II along a straight path, interacts with a bend in the fault or a branching junction. The experiments involved impact loading of thin Homalite-100 (a photoelastic polymer) plates, which had been cut along bent or branched paths and weakly glued back together everywhere except along a starter notch near the impact site. Strain gage recordings and high-speed photography of isochromatic lines provided characterization of the transient deformation fields associated with the impact and fracture propagation. We found that dynamic explicit 2-D plane-stress finite element analyses with a simple linear slip-weakening description of cohesive and frictional strength of the bonded interfaces can reproduce the qualitative rupture behavior past the bend and branch junctions in most cases and reproduce the principal features revealed by the photographs of dynamic isochromatic line patterns. The presence of a kink or branch can cause an abrupt change in rupture propagation velocity. Additionally, the finite element results allow comparison between total slip accumulated along the main and inclined fault segments. We found that slip along inclined faults can be substantially less than slip along the main fault, and the amount depends on the branch angle and kink or branch configuration.

MEASUREMENT OF CONTACT STRESSES USING REAL-TIME SHEARING INTERFEROMETRY

The optical method coherent gradient sensing, a real-time lat- eral shearing interferometry, is proposed for measuring contact stress fields under static and dynamic loading conditions. Feasibility of the method is first established under quasi-static conditions. Under dynamic conditions, the method has been used in conjunction with high-speed photography. The interference patterns representing stress gradients are used for extracting impact load history. Loading rates of approximately 14 MN/sec have been observed. The optical measurements are com- pared with the computed values obtained using finite element simula- tions.

Dynamic path selection along branched faults: Experiments involving sub‐Rayleigh and supershear ruptures

Building upon previous laboratory earthquake experiments of dynamic shear rupture growth taking place along faults with simple kinks, new and complex fault geometries involving cohesively held fault branches are studied. Asymmetric impact at the specimen boundaries controls the incoming shear ruptures, which are manipulated to propagate at either sub-Rayleigh or supershear velocities. High-speed photography and dynamic photoelasticity are used with a model material, Homalite-100, to monitor incoming and outgoing rupture propagation, acceleration, deceleration, or arrest at the vicinity of the branch location. Differences and similarities of rupture velocity history between cases involving faults with either simple kinks or branches, on the one hand, and sub-Rayleigh and supershear incoming ruptures, on the other, are highlighted and explained. Results of the experiments show a clear general bias toward large branch inclination, smaller branch angles appearing to be overshadowed and suppressed by the stress field associated with the main fault. Of great interest, also, is the sustenance of rupture propagation along a branch by the Mach cone, when the initial rupture is supershear driven. Generally, higher rupture speeds favors larger arrays of branching angles to be triggered. A companion analysis by Templeton et al. (2009) featuring detailed numerical simulations of these experiments provides further insight into the observed phenomena.