K. Ravi-Chandar

An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching

This is the third in a series of four papers in which problems of dynamic crack propagation are examined experimentally in large, thin sheets of Homalite-100 such that crack growth in an unbounded plate is simulated. In the first paper crack initiation resulting from stress wave loading to the crack tip as well as crack arrest were reported. It was found that for increasing rates of loading in the microsecond range the stress intensity required for initiation rises markedly. Crack arrest occurs abruptly without any deceleration phase at a stress intensity lower than that which causes initiation under quasi-static loading.In the second paper we analyze the occurrence of micro cracks at the front of the running main crack which control the rate of crack growth. The micro cracks are recorded by real time photography. By the same means it is shown that these micro cracks grow and turn away smoothly from the direction of the main crack in the process of branching.In the present paper we report results on crack propagation and branching. It is found that crack propagation occurs at a constant velocity although the stress intensity factor changes markedly. Furthermore, the velocity is determined by the stress wave induced intensity factor at initiation. The terminal velocity in Homalite-100 was found to be about half the Rayleigh wave speed (0.45 Cr). These observations are analyzed in terms of a microcrack model alluded to in the second paper of this series. A mechanism for crack branching is proposed which considers branching to be a natural evolution from a “cloud” of microcracks that accompany and lead the main crack. These results are believed to apply to quasi-brittle materials other than Homalite-100 and the reasons for this belief are discussed briefly in the first paper of this series.In the final paper of the series the effect of stress waves impinging on the tip of a rapidly moving crack is examined. Waves affect the velocity and the direction of propagation as well as the process of crack branching.

On crack-tip stress state: An experimental evaluation of three-dimensional effects

Abstract The extent of the region of three-dimensionality of the crack-tip stress field is investigated using reflected and transmitted caustics. The range of the applicability of two-dimensional near tip solutions is thus established experimentally. The experiments are performed using Plexiglass and high-strength 4340-steel compact tension specimens. A wide spectrum of thicknesses is investigated. At each thickness, measurements are performed at a variety of distances r from the crack tip, ranging from r/h = 0 to r/h = 2, where h is the specimen thickness. The results indicate that plane-stress conditions prevail at distances from the crack tip greater than half the specimen thickness, while no significant plane-strain region is detected. The experimental results are also compared to the crack-tip boundary-layer solution of Yang and Freund[1], and the numerical results of Levy, Marcal and Rice[2]. Their solutions are consistent with the results of this work and approach the plane stress field at r/h = 0.5. In addition, and unlike what might be commonly expected, the analytical solution[1] exhibits no plane-strain behavior very near the crack tip. This behavior is in good agreement with the results of both the transmission and the reflection experiments.

A cohesive zone model for fatigue crack growth in quasibrittle materials

Abstract A cohesive zone model for fatigue crack initiation and growth in quasibrittle materials is proposed in the present paper. While bulk material is modeled to be linearly elastic, the softening material in the cohesive zone and cracks are modeled to be internal singular surfaces in the elastic body. The interactions of the singular surfaces are described in a cohesive force law and a Coulomb-type friction law if in contact. The cohesive zone material is modeled to accumulate damage not only along the damage locus but also along an unloading path underneath it, enabling a simulation of fatigue damage and crack growth without the ad hoc imposition of a law of growth rate within the cohesive zone model. The maximum principal stress criterion is used to advance a tip of the cohesive zone in the direction of the maximum principal stress when it reaches the critical value of material strength. The physical crack tip is grown as a natural process of debonding of the cohesive zone under cyclic loading, which, in contrast, may be subcritical with energy dissipation less than the material toughness under static loading. The boundary value problem formulated for fatigue crack growth incorporating the cohesive zone model is nonlinear due to the history dependence of the cohesive zone, and is solved efficiently using the iterative single-domain dual-boundary-element method of successive over-relaxation. It is demonstrated through examples that the present model is capable of predicting fatigue crack initiation as well as growth in a unified way. It is also shown that the cohesive zone model is more advantageous and flexible in handling fatigue cracks under arbitrary loading than the classical singularity-based fracture mechanics approach.

Dynamic fracture of nominally brittle materials

Current understanding of dynamic fracture mechanisms and the methods of modeling are reviewed critically. Experimental methods used in dynamic fracture investigations and key experimental observations are reviewed. This is followed by a critical review of the dynamic fracture models. Mechanistic and phenomenological models as well as discrete and continuum models and their ability to reproduce experimental results are discussed.

On the role of microcracks in the dynamic fracture of brittle materials

Abstract The dynamic fracture behavior of brittle materials is investigated. The morphology of the fracture surface is examined in detail in four polymers: polymethylmethacrylate, Solithane-113, Homalite-100 and poly-carbonate. The fracture surface markings are examined to determine the micromechanisms of fracture. This examination reveals clearly that the operative micromechanism that governs dynamic fracture in brittle materials is the nucleation, growth and coalescence of microcracks. Following a quantitative characterization of the microcracking patterns, a very simple nucleation and growth model is then put forward. Imposing nucleation and growth criteria based on the experimental observations, the simulation recreates the experimental observations, not only of the microscope surface features, but also of the macroscopic behavior such as the constancy of the crack speed.

Evaluation of elastic T-stress by the stress difference method

Abstract A simple method, called the stress difference method , is proposed to compute the elastic T -stress at a crack tip, incorporating the iterative single-domain dual-boundary-element method and a tip-node rule imposing zero displacement jump at the crack tip. In this method, the difference between σ 11 and σ 22 at a point ahead of the crack tip is demonstrated to be able to evaluate the elastic T -stress efficiently and accurately, in comparison to the I -integral method. Convergence of the T -stress computed by this method with mesh and spatial distribution of σ 11 − σ 22 near a crack tip was examined to validate the numerical technique for the T -stress. When applying to a thermoelastic crack, the present stress difference method also shows good agreement with the corresponding I -integral method. On the other hand, the present inspection method for the T -stress is obviously more advantageous than the I -integral method because of its simplicity in expression and much less computational effort. It is also shown that the tip-node rule for the crack tip element with regular polynomial interpolation and node distribution offers good estimates of the stress intensity factor, in contrast to the quarter-point element method.

On the failure mode transitions in polycarbonate under dynamic mixed-mode loading

Abstract Polycarbonate is known to exhibit rate dependent inelastic behavior. In the present work, it is shown that under predominantly mode II loading, superposed with a hydrostatic compressive stress field, the rate dependence manifests itself in interesting failure mode transitions from ductile to brittle to ductile again. The second transition is quite unusual and is examined in light of the hydrostatic compression and thermal softening of the material.

Failure mode transitions in polymers under high strain rate loading

A rather unusual failure mode transition from brittle to ductile at high strain rates occurs under a combined pressure and shear loading. This transition also represents a change in the failure mode from a normal stress dominated fracture mode at low loading rates to a shear stress dominated shear banding failure at high strain rates. While most such observations have been in metallic materials, where such transitions are attributed to thermal softening caused by adiabatic heating, in this paper we present evidence of such mode transitions in a polymer. Experimental observations of the pressure-shear loading experiments are reported in two polymers; polycarbonate (PC) and polymethylmethacrylate (PMMA). Dynamic photomechanics techniques were used in obtaining information regarding the crack tip state in these experiments. While PC exhibits a failure mode transi- tion to shear banding, PMMA changes to a shear mode of fracture; dynamic shear fracture has been observed in real-time using high speed photography for the first time. A numerical simulation of the experiment using a simple constitutive description of the material is performed in order to gain an understanding of the evolution of the crack tip fields that generate the observed mode transitions. The results of the simulation suggest that thermal softening may not play a significant role in the failure mode transitions in polymers. On the other hand, it is shown that the competition between shear yielding and normal stress dominated fracture mechanisms is the key to the failure mode transitions in these polymers.

Dynamic Loading of Polycrystalline Shape Memory Alloy Rods

Abstract Shape memory alloys (SMAs) have recently been considered for dynamic loading applications for energy absorbing and vibration damping devices. An SMA body subjected to external dynamic loading will experience large inelastic deformations that will propagate through the body as phase transformation and/or detwinning shock waves. The wave propagation problem in a cylindrical polycrystalline SMA rod induced by an impact loading is considered in this paper. Numerical solutions for various boundary conditions are presented for stress induced martensite and detwinning of martensite. The numerical simulations utilize an adaptive finite element method (FEM) based on the Zienkiewicz–Zhu error estimator. Selected results are compared to known analytical solutions to verify the adaptive FEM approach. The energy dissipation in an SMA rod is evaluated for a square pulse stress input applied at various temperatures involving both stress induced martensite and detwinning of martensite. The dynamic response of a NiTi SMA rod is also studied experimentally in a split Hopkinson bar apparatus under detwinning conditions. Strain history records obtained by strain gauges placed at different locations along the SMA rod are compared with numerical simulations for a square pulse stress input. The quasi-static and dynamic stress–strain hysteretic response of the SMA, both due to detwinning, are found to be nearly identical. The quasi-static tests are used to calibrate the rate independent constitutive model used for the numerical simulations, which are found to match the experimental observations reasonably well.

Crack path instabilities in a quenched glass plate

A crack driven by steadily quenching a hot glass plate into a water bath exhibits fascinating path instabilities that depend on the severity of the temperature jump involved in the quenching process. An experimental and analytical investigation of these crack path instabilities is presented in this paper. First, real-time observations of the growth of the crack at different temperature jumps are presented. With increasing temperature jump, the crack path changes from a straight path to a periodic oscillatory path, then to a chaotic oscillatory path, to an unstable (dynamic) straight crack path, and finally to multiple crack paths. The experimental observations show that the crack growth is not a steady process even though the quenching occurs at a constant speed. The experimental observations provide crucial insight and the basis for the analysis of the problem. The problem is then examined analytically by solving the underlying thermoelastic problem, within the framework of linear elastic fracture mechanics. The results of the numerical simulations in conjunction with the experimental observations are used to show that (i) the T-stress criterion commonly used for evaluating crack path instability is inapplicable to this problem, (ii) the crack path stability can be determined by using the maximum tangential stress criterion for crack advance and examining the divergence of adjacent crack paths, (iii) the initiation of a structurally unstable crack can be determined, and (iv) the complete oscillatory crack path can be obtained through an incremental solution of the thermoelastic problem.