B.S. Majumdar

Crack tip shielding—An elastic theory of dislocations and dislocation arrays near a sharp crack☆

An elastic solution has been found for a screw dislocation near a crack in the absence of any external stresses. The dislocation produces a stress intensity factor on the crack even without external stresses. The stress intensity factor at the crack tip plus the dislocations contribution to the stress intensity factor add to the stress intensity factor due to the applied stresses. Also the interaction between the crack and dislocations, and between dislocations in the presence of the crack can be solved by simply considering the associated stress intensity factors at the crack tip. Several additional solutions derived are two dislocations at the crack tip, a dislocation off the crack plane, a circle of dislocations around the crack tip and a finite length crack with external stresses.

Interfacial debonding analysis in multiple fiber reinforced composites

Decohesion at multiple fiber interfaces of elastic fiber reinforced composites is modeled by the Voronoi cell finite element model (VCFEM) in this paper. Interfacial debonding is accommodated by cohesive zone models, in which normal and tangential springs tractions are expressed in terms of interfacial separation. Model simulations are compared with results from experiments using cruciform specimens, of single and multiple fiber polymer-matrix composites. An inverse problem is solved to calibrate the cohesive zone parameters. Debonding at fiber-matrix interfaces is simulated for different architectures, volume fractions and boundary conditions, to understand the influence of microstructural morphology and boundary conditions on the decohesion process.

Laminated particulate-reinforced aluminum composites with improved toughness

Abstract An architectural approach for toughening discontinuously reinforced aluminum (DRA) alloys is described. It is based upon exploiting the higher apparent toughness of thin DRA lamina to obtain a laminate of higher thickness and toughness. The laminated composite consisted of alternate layers of a 7093/SiC/15p DRA, and an unreinforced aluminum–manganese alloy, 3003. Fracture toughness tests in the crack divider configuration showed a toughness improvement of 79% in an underaged condition and an improvement of 53% in the peak-aged condition compared to the monolithic DRA. Fractographic observations of the primary void size, and its close correspondence with the fracture surface of thin specimens, provided evidence that the individual DRA lamina indeed experienced sufficient loss of constraint in the thickness direction. This was further confirmed by observations of delamination in the fast fracture domain. However, the bond strength was quite good, as evidenced by very little delamination in the fatigue crack growth region, and by a lack of such damage in tension specimens. In essence, the laminate behaved as a smart structure, being resistant to failure under normal conditions, but allowing full loss of constraint in the severe stress–strain field ahead of a loaded crack. Modeling efforts were consistent with a reduction of hydrostatic stress, through the loss of out-of-plane constraint for the laminas, although the predicted level of toughness improvement was lower than observed. Overall, this study clearly demonstrates that the fracture toughness of laminated composites can be engineered based on the understanding of constraint effects associated with specimen thickness in the DRA composite.

Effect of aluminum particles on the fracture toughness of a 7093/SiC/15p composite

Abstract The effects of Al-particles on the toughness of a discontinuously reinforced aluminum (DRA) alloy composite were studied in this investigation. A powder metallurgically processed ‘control’ DRA consisting of 7093/SiC/15p (10 μm) was selected as the base material. The remaining DRAs contained aluminum particles of different size, volume fraction and composition, that were blended with the base DRA, and powder metallurgically processed and extruded; they are termed as ‘bean’ materials. The modulus, yield strength, and work hardening rate of the bean materials with Al-alloy particles were quite insensitive to the distribution of the SiC particles. On the other hand, the strain to failure was most strongly influenced by the presence of pure-Al and Al-alloy particles, and is explained based on the local SiC particle volume fraction. Fracture toughness calculations show that the ASTM E-561 procedure is more appropriate for DRA materials, that exhibit small scale yielding conditions, than ASTM E-813 and E-1152 procedures. The bean materials exhibited improved crack growth toughnesses over the control DRA, and in some cases the initiation toughness was also increased. The toughening mechanisms are discussed.

Stress distribution in a transversely loaded cross-shaped single fiber SCS-6/Ti-6Al-4V composite

In most structural applications utilizing fiber reinforced metal matrix composites (MMCs), the mechanical response normal to the fiber direction has to be considered. The transverse response is very sensitive to the interface bond strength, which has commonly been determined by testing straight-sided 90{degree} specimens and interpreting debond initiation from the knee in the stress-strain curve as well as from a sudden drop in the Poisson`s ratio. In an attempt to modify the debond initiation site to an internal location free of uncharacteristic states of stress, a cross-shaped specimen has been developed. Experiments conducted by Gundel et al. indicated that this geometry was successful in obtaining the appropriate crack initiation site. In the present study, finite element analysis (FEA) was done on the cross-shaped specimen to obtain the stress distribution in the composite under transverse loading, in an effort to corroborate the success of this geometry in determining the true transverse response of the composite.

Measurement of the state of stress in silicon with micro-Raman spectroscopy

Micro-Raman spectroscopy has been widely used to measure local stresses in silicon and other cubic materials. However, a single (scalar) line position measurement cannot determine the complete stress state unless it has a very simple form such as uniaxial. Previously published micro-Raman strategies designed to determine additional elements of the stress tensor take advantage of the polarization and intensity of the Raman-scattered light, but these strategies have not been validated experimentally. In this work, we test one such stategy [S. Narayanan, S. Kalidindi, and L. Schadler, J. Appl. Phys. 82, 2595 (1997)] for rectangular (110)- and (111)-orientated silicon wafers. The wafers are subjected to a bending stress using a custom-designed apparatus, and the state of (plane) stress is modeled with ABAQUS. The Raman shifts are calculated using previously published values for silicon phonon deformation potentials. The experimentally measured values for σxx, σyy, and τxy at the silicon surface are in good ag...

Analysis of R-curve behavior of non-phase-transforming ceramics

Abstract An analysis is presented of the phenomenon of increased crack resistance with crack growth ( R- curve behavior) exhibited by ceramics such as alumina, which do not undergo phase-transformation in the process and by ceramic-matrix composites. These materials contain a wake of unbroken ligaments and crack bridges, and these are modeled in this paper to account for R- curve behavior. The analysis is based on a modified Dugdale strip yield model. Various sizes and geometries of specimens are analysed, and a small-scale yielding estimation is also presented. Good correlation is obtained between predicted and experimental R- curve behavior. The model is also used to predict the dependence of saturation fracture toughness on grain size.

Deformation and fracture of a particle-reinforced aluminum alloy composite: Part I. Experiments

Mechanical tests were performed on a powder-metallurgically processed 7093/SiC/15p discontinuously reinforced aluminum (DRA) composite in different heat-treatment conditions, to determine the influence of matrix characteristics on the composite response. The work-hardening exponent and the strain to failure varied inversely to the strength, similar to monolithic Al alloys, and this dependence was independent of the dominant damage mode. The damage consisted of SiC particle cracks, interface and near-interface debonds, and matrix rupture inside intense slip bands. Fracture surfaces revealed particle fracture-dominated damage for most of the heat-treatment conditions, including an overaged (OA) condition that exhibited a combination of precipitates at the interface and a precipitate-free zone (PFZ) in the immediate vicinity. In the highly OA conditions and in a 450 °C as-rolled condition, when the composite strength became less than 400 MPa, near-interface matrix rupture became dominant. A combination of a relatively weak matrix and a weak zone around the particle likely contributed to this damage mode over that of particle fracture. Fracture-toughness tests show that it is important to maintain a proper geometry and testing procedure to obtain valid fracture-toughness data. Overaged microstructures did reveal a recovery of fracture toughness as compared to the peak-aged (PA) condition, unlike the lack of toughness recovery reported earlier for a similar 7XXX (Al-Zn-Cu-Mg)-based DRA. The PA material exhibited extensive localization of damage and plasticity. The low toughness of the DRA in this PA condition is explored in detail, using fractography and metallography. The damage and fracture micromechanisms formed the basis for modeling the strength, elongation, toughness, and damage, which are described in Part II of this work.

A micromechanical model for cleavage-crack reinitiation

A crack-tip screening analysis of cleavage fracture of steel is developed. The analysis incorporates evidence that reinitiation of an arrested cleavage crack requires less stress intensity than cleavage initiation from a fatigue precrack. Fractographic evidence as well as metallographic sectioning of arrested cracks have previously shown that the mechanism of rapid crack propagation by cleavage is affected strongly by partial crack-plane deflection which leaves unbroken ligaments in its wake. The tearing of these ligaments by dimple rupture is the dominant energy-absorbing mechanism. Earlier etch-pit experiments using an Fe-Si alloy showed that the crack-tip stress intensity based on plastic zone size is extremely low. These observations are incorporated into a model in which cleavage crack reinitiation is analyzed using a sharp crack that is shielded by a distribution of pinching forces along its faces. During reloading of the arrested crack, the ligaments restrict crack-tip blunting, leading to higher local stresses. As a result, lower stress intensities are needed for reinitiation than for initiation from a fatigue precrack.

Interface effects on the micromechanical response of a transversely loaded single fiber SCS-6/Ti-6Al-4V composite

The ability of a fiber-matrix interface to support a transverse load is typically evaluated in straight-sided composite specimens where a stress singularity exists at the free surface of the interface. This stress singularity is often the cause of crack initiation and debonding during transverse loading. In order to develop a fundamental understanding of the transverse behavior of the fiber-matrix interface, it is necessary to alter the crack initiation site from the free surface to an internal location. To achieve this objective, a cross-shaped specimen has been recently developed. In this study, based on the experimentally observed onset of nonlinearity in the stress-strain curve of these specimens and finite element analysis, the bond strength of the SCS-6/Ti-6Al-4V interface was determined to be 115 MPa. The micromechanical behavior of these specimens under transverse loading was examined by finite element analysis using this interface bond strength value and compared with experimental observations. Results demonstrate that the proposed geometry was successful in suppressing de-bonding at the surface and altering it to an internal event. The results from numerical analysis correlated well with the experimental stress-strain curve and several simple analytical models. In an attempt to identify the true bond strength and the interface failure criterion, the present study suggests that if failure initiates under tensile radial stresses, then the normal bond strength of the SCS-6/Ti-6A1-4V composites is about 115 MPa; under shear failure, the tangential shear strength of the in-terface is about 180 MPa.