Critical Stress Criterion Research Articles

Fracture modes in brittle coatings with large interlayer modulus mismatch

Fracture modes in a model glass–polymer coating–substrate system indented with hard spheres are investigated. The large modulus mismatch between the glass and polymer results in distinctive transverse fracture modes within the brittle coating: exaggerated circumferential (C) ring cracks that initiate at the upper coating surface well outside the contact (as opposed to the near-contact Hertzian cone fractures observed in monolithic brittle materials); median–radial (M) cracks that initiate at the lower surface (i.e., at the substrate interface) on median planes containing the contact axis. Bonding between the coating and substrate is sufficiently strong as to preclude delamination in our system. The transparency of the constituent materials usefully enables in situ identification and quantification of the two transverse fracture modes during contact. The morphologies of the cracks and the corresponding critical indentation loads for initiation are measured over a broad range of coating thicknesses (20 mm to 5.6 mm), on coatings with like surface flaw states, here ensured by a prebonding abrasion treatment. There is a well-defined, broad intermediate range where the indented coating responds more like a flexing plate than a Hertzian contact, and where the M and C cracks initiate in close correspondence with a simple critical stress criterion, i.e., when the maximum tensile stresses exceed the bulk strength of the (abraded) glass. In this intermediate range the M cracks generally form first—only when the flaws on the lower surface are removed (by etching) do the C cracks form first. Finite element modeling is used to evaluate the critical stresses at crack initiation and the surface locations of the crack origins. Departures from the critical stress condition occur at the extremes of very thick coatings (monolith limit) and very thin coatings (thin-film limit), where stress gradients over the flaw dimension are large. Implications of the results concerning practical coating systems are considered.

Study of the mechanical properties of Mg-7.7at.% Al byin-situneutron diffraction

Abstract Internal stresses in tension and compression in an extruded and artificially aged Mg-7.7at.% Al alloy have been determined by in-situ neutron diffraction. Measurements were made on grains having the c axis normal to, parallel to and at 62° from the stress axis, and on the reinforcing phase. The results are consistent with basal slip and {1012} twinning. The second-phase particles of Mg17Al12 bear much higher stresses than the magnesium matrix does. A simple mean stress model proposed by Brown and Clarke is shown to describe adequately the strengthening due to the particles. Twinning manifests itself clearly through variations in the integrated intensity of diffraction peaks during loading. Most of the observed variations in scattered peak intensity can be explained by referring to the lattice reorientation produced by {1012} twinning. The calculated stress tensors corresponding to these intensity variations have been used to show that a critical resolved shear stress criterion is applicable for {...

Study of the mechanical properties of Mg-7.7at.% Al by in-situ neutron diffraction

Abstract Internal stresses in tension and compression in an extruded and artificially aged Mg-7.7at.% Al alloy have been determined by in-situ neutron diffraction. Measurements were made on grains having the c axis normal to, parallel to and at 62° from the stress axis, and on the reinforcing phase. The results are consistent with basal slip and {1012} twinning. The second-phase particles of Mg17Al12 bear much higher stresses than the magnesium matrix does. A simple mean stress model proposed by Brown and Clarke is shown to describe adequately the strengthening due to the particles. Twinning manifests itself clearly through variations in the integrated intensity of diffraction peaks during loading. Most of the observed variations in scattered peak intensity can be explained by referring to the lattice reorientation produced by {1012} twinning. The calculated stress tensors corresponding to these intensity variations have been used to show that a critical resolved shear stress criterion is applicable for {1012} twinning, and that the onset of twinning does not correlate with the stress normal to the twin plane. Intensity variations, which cannot be explained by {1012} twinning, occurred in cyclic tension tests. It is suggested that this is due to {1011} twinning, which yields a contribution to the grain strain tensor consistent with the direction of straining. The reason why such twinning has not been observed in polycrystalline samples by previous workers is that it appears to be essentially elastic, in the sense that it disappears almost entirely upon removal of the applied stress.

Void-nucleation vs void-growth controlled plastic flow localization in materials with nonuniform particle distributions

Plastic flow localization may occur after significant void growth or immediately after void nucleation. In the present work, a model is developed to investigate the role of nonuniform particle distributions (e.g. random distribution, clusters) in plastic flow localization. A parameter is developed to quantitatively determine whether localization is predominantly controlled by void-nucleation or by void-growth. It is established that, for large clusters of particles, localization is more likely to be initiated by void nucleation, while it is dominated by void growth for small clusters. Both critical strain and stress void-nucleation criteria are investigated. It is observed that void-nucleation governed by the critical stress criterion initiates plastic flow localization at a much lower strain level than that governed by the critical strain criterion.

Response of fiber reinforced ceramic matrix composites through computational modeling of damage

Uni-axial tension experiments with a uni-directional ceramic matrix composite have indicated which damage mechanisms are active during the deformation history. A finite element model has been developed to investigate the onset and evolution of these experimentally observed damage mechanisms in a unit cell. This computational model is based on an axisymmetric unit cell which is discretized into cohesive interface elements and linearly elastic elements. As cohesive elements fail according to critical stress and energy release rate criteria, cracks form and propagate. To obtain converged solutions during crack propagation the full dynamic equations were solved implicitly using the Newmark method. The unit cell response was determined as a function of the fiber/matrix interface strength and toughness and as a function of the matrix toughness. Details of matrix crack propagation and the subsequent debond initiation were observed, and the implications for material toughening are discussed. The simplest unit cell response was averaged using the experimentally determined evolution of matrix crack density. The averaged response of the unit cell corresponds very well to the experimentally measured macroscopic composite response.

Computational modeling of damage evolution in unidirectional fiber reinforced ceramic matrix composites

A finite element model for investigating damage evolution in brittle matrix composites was developed. This modeling is based on an axisymmetric unit cell composed of a fiber and its surrounding matrix. The unit cell was discretized into linearly elastic elements for the fiber and the matrix and cohesive elements which allow cracking in the matrix, fiber-matrix interface, and fiber. The cohesive elements failed according to critical stress and critical energy release rate criteria (in shear and/or in tension). The tension and shear aspects of failure were uncoupled. In order to obtain converged solutions for the axisymmetric composite unit cell problem, inertia and viscous damping were added to the formulation, and the resulting dynamic problem was solved implicitly using the Newmark Method. Parametric studies of the interface toughness and strength and the matrix toughness were performed. Details of the propagation of matrix cracks and the initiation of debonds were also observed.

Hygrostress-multicrack formation and propagation in cylindrical viscoelastic food undergoing heat and moisture transfer processes

Several foods stress-crack during heat and moisture transfer processes without careful process control. Since published simulation studies on stress-cracking were scarce, the present study aimed to develop and validate a model for simulating heat and moisture transfer, hygrostress crack formation and propagation in cylindrical, viscoelastic food. For this, an improved Luikov's model for heat and moisture transfer was used together with the virtual work principle of a viscoelastically deforming body, a critical tensile stress criterion for stress crack formation and a crack-tip-opening-angle criterion for stress crack propagation.

The effect of hydrogen on the fracture toughness of alloy X-750

The effect of hydrogen on the fracture toughness behavior of a nickel-base superalloy, Alloy X-750, in the solutionized and aged condition was investigated. Notched bend specimens were tested to determine if the fracture process was stress or strain controlled. The fracture was observed to initiate at a distance between the location of maximum stress and maximum strain, suggesting that fracture required both a critical stress and strain. The effect of hydrogen was further investigated and modeled using fracture toughness testing and fractographic examination. The fracture toughness of the non-charged specimen was 147 \(MPa\sqrt m \). Charging with hydrogen decreased the fracture toughness, Klc, to 52 \(MPa\sqrt m \) at a rapid loading rate and further decreased the toughness to 42 \(MPa\sqrt m \) for a slow loading rate. This is consistent with the rate-limiting step forthe embrittlement process being hydrogen diffusion. The fracture morphology for the hydrogen-charged specimens was intergranular ductile dimple, while the fracture morphology of noncharged specimens was a mixture of large transgranular dimples and fine intergranular dimples. The intergranular failure mechanism in Alloy X-750 was a microvoid initiation process at grain boundary carbides followed by void growth and coalescence. One role of hydrogen was to reduce the void initiation strain for the fine intergranular carbides. Hydrogen may have also increased the rate of void growth. The conditions ahead of a crack satisfy the critical stress criterion at a much lower applied stress intensity factor than for the critical fracture strain criterion. A model based on a critical fracture strain criterion is shown to predict the fracture behavior.

Effects of Crack Depth, Specimen Size, and Out-of-Plane Stress on the Fracture Toughness of Reactor Vessel Steels

Cleavage fracture toughness values for A533-B reactor pressure vessel (RPV) steel at -40°C obtained from test programs at Oak Ridge National Laboratory (ORNL) and University of Kansas (KU) are interpreted using the J-A2 analytical model. The KU test data are from smaller SENB specimens with a/w = 0.1 and 0.5. The ORNL test data are from 1) larger SENB specimens with a/w = 0.1 and 0.5, and 2) a six-point-bend cruciform specimen under either uniaxial or bi-axial loads. The analytical model is based on the critical stress criterion and takes into consideration the constraint effect using the second parameter A2 in addition to the generally accepted loading parameter J. It is demonstrated that the effects of crack depth (shallow versus deep), specimen size (small versus large), and loading type (uniaxial versus biaxial) on the fracture toughness from the test programs can be interpreted and predicted.

The effect of residual stress on the adhesion of PECVD-coated aluminum oxide film on glass

Transparent, amorphous and hard aluminum oxide films were deposited on glass at low temperatures (≤ 773 K) by r.f. plasma-enhanced chemical vapor deposition with AlCl 3, H 2 and CO 2 as the reactants. The adhesion of films, a predominant factor in determining the performance and reliability of a coating-substrate system, evaluated by the critical load in scratch testing strongly depends on the deposition conditions (substrate temperature and CO 2 flow rate) and compressive residual stress in the films measured by radii of curvature determinations. These films have shown a tensile cracking failure mode in scratch testing and as opposed to the prediction based on energy balance and the critical shear stress criteria, which indicates that the critical load will vary inversely with internal stress, the compressive residual stresses increase the adherence strength by increasing the resistance to the tensile cracking failure. Hence, it is important to characterize the failure modes associated with the scratch adhesion test to account for the dependence of critical load on internal stresses in the films.

Critical stress criteria for interfacial cavitation in MMCs

Density measurements and microstructural examinations have been used to follow the formation, growth and coalescence of cavities during tensile loading of metal matrix composites (MMCs). Finite element modelling has been used to predict the stress states around reinforcements of various shapes. The positions of peak hydrostatic and normal stress components at the interface have been compared with the microstructural sites where voids were found to form experimentally in aluminium reinforced with alumina particles or fibres. It is concluded that cavities form when a critical hydrostatic stress is reached.

The initiation of delayed hydride cracking at a blunt flaw

As part of a recently formulated research programme on the initiation of delayed hydride cracking (DHC) at a blunt flaw, the present paper's theoretical analyses show that, for a wide range of flaw geometry-material-applied loading combinations, the position of the stress maximum is unaltered as a consequence of the material being hydrided. This result provides a degree of underpinning for the concept that DHC initiation can be predicted using a critical threshold stress criterion, with the peak stress in the vicinity of a flaw tip being calculated on the basis that the material is unhydrided. For a wide range of flaw geometries, and assuming a constant-thickness hydrided region, the hydride-induced compressive stress σ H at a flaw root is relatively insensitive to the flaw geometry. The σ H-hydrided region length ( l relation is approximately the same as it is for a hydrided region at a smooth surface. Hydriding can reduce the stress at a flaw root by substantial amounts, the stress reduction increasing as the length of hydrided region decreases. Such a result, if coupled with results from diffusion-type calculations, could allow us to estimate the effect of thermal cycles on the maximum stress.

Fracture mechanical modeling of brittle fracture propagation and arrest of steel (1)

A model is proposed which simulates brittle fracture propagation and arrest of steel with finite thickness. Based on the critical stress criterion for brittle fracture and on stress field solution for dynamically running crack in an elastic-plastic solid, dynamic fracture toughness (KD) is calculated as a function of temperature and crack velocity. The calculated KD once decreases and then increases with increasing crack velocity. Upper limit crack velocity coincides with the plastic surface wave speed and decreases with increasing temperature. The predicted dependencies of KD on temperature and crack velocity agree with previously established experimental data. Effects of side-ligament formed near the plate surface and crack-tunneling at the inside of the plate are also taken into account for simulating the brittle crack propagation. The model predicts crack velocity, shear lip thickness, aspect ratio of the tunneling crack from the fundamental mechanical properties of steel. The model also predicts a lower bound value of applied stress intensity factor and crack velocity, the former of which may correspond to the arrest toughness, Kca.

Analysis of the notch tip damage zone in biaxially oriented polypropylene

AbstractThe circular notch tip damage zone in biaxially oriented polypropylene has been analyzed using a thickness correction to the elastic stress distribution for a sharp‐notched tension specimen. The size and shape of the damage zone as a function of applied stress followed a critical mean stress criterion, independent of specimen thickness. Also, the damage zone only grew while σ3 was greater than zero. Close observations of sections through the damage zone revealed that the circular zone, which consisted of many delamination crazes, had a distinctive pattern when viewed across the thickness difection. Large crazes grew into a triangular pattern with smaller crazes in between them. The shape developement of the triangular profile as well as the smaller crazes was explained using a stress‐redistribution argument. The growth path of the delamination crazes in the x‐z plane appeared to be in a direction perpendicular to the direction of σ3. © 1994 John Wiley & Sons, Inc.

Multilayer extrusion: Experiments and computer simulation

AbstractA mathematical model is presented for the computer simulation of multilayer flow of polymer melts in coexitrusion. The proposed model can handle an arbitrary number of layers. The viscosity of each layer is shear‐rate and temperature dependent. Given the material properties, die dimensions, and process conditions, the model determines the flow field throughout the die gap. Computer simulations and experimental data are presented for a three‐layer polyester/EVA/polyester film coextrusion, with emphasis on the interfacial instability and its effects on optical properties of the film. The rsults are discussed in the context of the critical interfacial shear stress criterion that has been proposed by Schrenk, et al. (1) for the onset of interfacial instability. It appears that elasticity differences between layers contribute to the interfacial instability. It is conjectured that minimizing interfacial shear stress and matching elasticities of adjacent layers is an appropriate criterion in coextrusion analysis.

On pressure-shear plate impact for studying the kinetics of stress-induced phase transformations

Pressure-shear plate impact experiments are proposed for studying the kinetics of stress-induced phase transformations. The purpose of this paper is to determine loading conditions and specimen orientations which can be expected to activate a single habit plane variant parallel to the impact plane, thereby simplifying the study of the kinetics of the transformation through monitoring the wave profiles associated with the propagating phase boundary. The Wechsler-Lieberman-Read phenomenological theory was used to determine habit plane indices and directions of shape deformation for a CuAlNi shape memory alloy which undergoes a martensitic phase transformation under stress. Elastic waves generated by pressure-shear impact were analyzed for wave propagation in the direction of the normal to a habit plane. A critical resolved shear stress criterion was used to predict variants which are expected to be activated for a range of impact velocities and relative magnitudes of the normal and transverse components of the impact velocity.

Effects of shear stresses on crack-growth microstructures in transformation-toughened ceramics

Abstract In accordance with a prior study, transformation toughening of zirconia-reinforced ceramics is simulated by treating regions of particles surrounding quasi-statically advancing cracks as Mode-I symmetric distributions of circular spots that undergo a ‘supercritical’ dilatant transformation when a critical stress criterion is satisfied. Three stress criteria are considered: mean stress, maximum in-plane shear stress, and an equal mixture of these two. Simulations with the mean-stress criterion show good agreement with results of previous continuum-based analyses, as the profile of the transformed region ahead of the tip approximates a partial cardioid. In contrast, simulations for the other criteria display claw-like transformed regions extending far ahead of the crack tip. This difference in behaviour is conjectured to arise from the presence of direct spot-to-spot interaction terms in the shear stress and may account for large (i.e. mm size) transformed regions seen in some materials.

Abrasive wear and craze breakdown in polystyrene

The role of craze breakdown during the fracture process of abrasive wear in glassy polystyrene was investigated. At first, the wear resistance, γw, was compared with the craze breakdown strain as a function of molecular weight and diluent concentration. It was found that γw increases with molecular weight and decreases with the diluent concentration. Although craze breakdown strain also increases with molecular weight and decreases with the diluent concentration, the wear data do not converge into a single curve in a plot against the craze breakdown strain. Selected specimens were then studied by micro-indentation and micro-scratching experiments. An analysis of the scratch patterns and contact load at the polymer surface indicated that a critical stress criterion, rather than a critical strain criterion, may be suitable for the onset of the failure process in brittle polymer wear. With this criterion, the critical load for crack opening, τc, can be related to the craze breakdown strain and Young's modulus, and the observed deviation between the craze breakdown strain and γw can be explained.

Prediction of matrix-particle interfacial separation in particle-strengthened materials

The phenomenology of local interfacial separation between elastic second-phase particles and the plastic matrix was analysed in this study. Previous analyses characterizing the interfacial stress, σ n developed around particles were first assessed. Next, a modified dislocation model reflecting local microscopic matrix deformation behaviour around non-deformable particles was introduced to calculate σ n and to compare with earlier continuum analysis results. The model was applied to the case of rigid carbide particles based on a critical stress criterion for interfacial debonding. Also, an attempt was made to interpret the progress of microcavity initiation at the particle interface in terms of a normal distribution function of microcavity volume density.

Void nucleation in constrained silver interlayers

The process of void nucleation during fracture in thin brazed Ag interlayers has been investigated. Tensile tests were performed on interlayers of five thicknesses. The tensile strength increased rapidly with the ratio of interlayer diameter to thickness(D/T) for the thick interlayers(D/T < approximately 40) while the rate decreased significantly in the thin interlayers. All specimens fractured in the Ag interlayer along a plane near, and parallel to, the steel interface. The fracture surfaces showed silicon oxide inclusions at the bottom of many of the dimples. A series of finite element models were constructed to determine the general stress state in the interlayers and to determine the development of local stresses around inclusions in the interlayer. The finite ele- ment calculations indicated that the distribution of triaxial tension radially across the interlayer varied withD/T. Triaxial stresses, at failure, up to 10 times the uniaxial yield stress of the Ag were predicted from the model. The local stresses around a rigid inclusion in the interlayer developed more quickly, with applied stress, in the thicker interlayers as a result of the increased plastic deformation. The development of local stresses also increased with the proximity of the inclusion to the steel interface. By assuming a critical stress criterion for void nucleation at an inclusion interface, the finite element model was able to predict the experimentally observed nonlinear relationship between the interlayer failure stress andD/T.