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At least 307 records · Page 17

Fracture modes and acoustic emission of composite materials

Unidirectional fibrous composite material laminae are the construction material of a laminate. Four failure modes can occur in this material, and the identification of these modes is as important as the identification of onset of fracture. Acoustic emission (AE) pulses, generated by the change in the stress field resulting from cracking in a material, have a unique pattern of amplitude distribution that depends only on the mode of fracture and the type of material. By using a tapered double-cantilever beam as grips for the unidirectional lamina, a crack with a constant stress intensity factor was induced, thus eliminating the factor of the stress level. Placing the lamina in different directions relative to the grips imposed a different failure mode. By plotting the log of the relative number of AE pulses above some level versus the log of the relative level, a single constant coefficient can be measured for each material and mode of fracture. The AE energy is proportional to the energy released by the cracking; this proportionality depends on the medium where the AE waves have to travel, and not on the cracking mode.

Rotem, A.↗

Sudden stretching of a four layered composite plate

An approximate theory of laminated plates is developed by assuming that the extensioral and thickness mode of vibration are coupled. The mixed boundary value crack problem of a four layered composite plate is solved. Dynamic stress intensity factors for a crack subjected to suddenly applied stress are found to vary as a function of time and depend on the material properties of the laminate. Stress intensification in the region near the crack front can be reduced by having the shear modulus of the inner layers to be larger than that of the outer layers.

Sih, G. C.↗

The crack problem for a half plane stiffened by elastic cover plates

An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.

Delale, F.↗

Moving cracks in layered composites

A three-layered composite with a crack spreading in the center layer has been analytically examined to evaluate the effect of material nonhomogeneity on a constant velocity crack. Two different loading characteristics are considered. In the first case, crack motion is maintained by uniform tensile stresses. In the other, crack deformation is caused by anti-plane shear stresses. Galilean transformation and Fourier sine and cosine transforms are used to determine dynamic crack tip stress fields. Standard Fredholm integral equations yield the dynamic stress intensity factors. The results show that the intensity of local dynamic stresses increases or decreases with crack length to layer thickness as a function of the relative magnitudes of the adjoining layer's material properties. Crack speed tends to increase the effect of material nonhomogeneity.

Sih, G. C.↗

A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity

A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

Wang, S. S.↗

A review of fracture mechanics life technology

Current lifetime prediction technology for structural components subjected to cyclic loads was reviewed. The central objectives of the project were to report the current state of and recommend future development of fracture mechanics-based analytical tools for modeling and forecasting subcritical fatigue crack growth in structures. Of special interest to NASA was the ability to apply these tools to practical engineering problems and the developmental steps necessary to bring vital technologies to this stage. A survey of published literature and numerous discussions with experts in the field of fracture mechanics life technology were conducted. One of the key points made is that fracture mechanics analyses of crack growth often involve consideration of fatigue and fracture under extreme conditions. Therefore, inaccuracies in predicting component lifetime will be dominated by inaccuracies in environment and fatigue crack growth relations, stress intensity factor solutions, and methods used to model given loads and stresses. Suggestions made for reducing these inaccuracies include: development of improved models of subcritical crack growth, research efforts aimed at better characterizing residual and assembly stresses that can be introduced during fabrication, and more widespread and uniform use of the best existing methods.

Thomas, J. M.↗

A review of fracture mechanics life technology

Lifetime prediction technology for structural components subjected to cyclic loads is examined. The central objectives of the project are: (1) to report the current state of the art, and (2) recommend future development of fracture mechanics-based analytical tools for modeling subcritical fatigue crack growth in structures. Of special interest is the ability to apply these tools to practical engineering problems and the developmental steps necessary to bring vital technologies to this stage. The authors conducted a survey of published literature and numerous discussions with experts in the field of fracture mechanics life technology. One of the key points made is that fracture mechanics analyses of crack growth often involve consideration of fatigue and fracture under extreme conditions. Therefore, inaccuracies in predicting component lifetime will be dominated by inaccuracies in environment and fatigue crack growth relations, stress intensity factor solutions, and methods used to model given loads and stresses. Suggestions made for reducing these inaccuracies include development of improved models of subcritical crack growth, research efforts aimed at better characterizing residual and assembly stresses that can be introduced during fabrication, and more widespread and uniform use of the best existing methods.

Besuner, P. M.↗

A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity

A simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems is presented. The analysis is formulated on the basis of conservation laws of elasticity and of fundamental relationships in fracture mechanics. The problem is reduced to the determination of mixed-mode stress-intensity factor solutions in terms of conservation integrals involving known auxiliary solutions. One of the salient features of the present analysis is that the stress-intensity solutions can be determined directly by using information extracted in the far field. Several examples with solutions available in the literature are solved to examine the accuracy and other characteristics of the current approach. This method is demonstrated to be superior in its numerical simplicity and computational efficiency to other approaches. Solutions of more complicated and practical engineering fracture problems dealing with the crack emanating from a circular hole are presented also to illustrate the capacity of this method

Yau, J. F.↗

Strength characteristics and crack growth behavior of a composite with well aligned fibers

Continuous fiber composites have shown tremendous promise in industrial applications. Their microstructures, however, are very complex and in many instances difficult to characterize. In this project, the fracture characteristics of a specially made fiber reinforced composite with different fiber spacing are investigated. The experimental results so far have shown that after an initial transient phase the crack speed reaches a steady phase, i.e., independent of the crack length. Within the steady crack growth phase debonding along the fibers in the bridging zone grows in a self-similar manner. During the steady phase the energy dissipation per cycle is constant. Afterwards, an increase of the energy dissipation is observed that is accompanied by a decrease in crack speed. This latter trend is presumed to be the result of relatively large amounts of energy dissipated in the bulk of the specimen. Using appropriate Green's function and computer simulations, the stress intensity factor at the crack tip is evaluated for various cases of bridging stresses. In this way the effects of specimen size and fiber spacing on the overall fracture behavior of the composite system are analyzed. The steady crack speed and the steady rate of debonding have a similar power dependence on stress level. Dimensional analysis demonstrates that the particular fracture process is not governed by dimensional invariance but on the detailed micromechanisms in the bridging zone.

Botsis, John↗

Variations of a global constraint factor in cracked bodies under tension and bending loads

Elastic-plastic finite-element analyses were used to calculate stresses and displacements around a crack in finite-thickness plates for an elastic-perfectly plastic material. Middle- and edge-crack specimens were analyzed under tension and bending loads. Specimens were 1.25 to 20 mm thick with various widths and crack lengths. A global constraint factor alpha(sub g), an averaged normal-stress to flow-stress ratio over the plastic region, was defined to simulate three-dimensional (3D) effects in two-dimensional (2D) models. For crack lengths and uncracked ligament lengths greater than four times the thickness, the global constraint factor was found to be nearly a unique function of a normalized stress-intensity factor (related to plastic-zone size to thickness ratio) from small- to large-scale yielding conditions for various specimen types and thickness. For crack length-to-thickness ratios less than four, the global constraint factor was specimen type, crack length and thickness dependent. Using a 2D strip-yield model and the global constraint factors, plastic-zone sizes and crack-tip displacements agreed reasonably well with the 3D analyses. For a thin sheet aluminum alloy, the critical crack-tip-opening angle during stable tearing was found to be independent of specimen type and crack length for crack length-to-thickness ratios greater than 4.

Newman, J. C., Jr.↗

Stress analysis of cracks

Elastic stress analyses of cracked bodies represented by stress intensity factor method - fracture mechanics

STRESS ANALYSIS↗

Strain buildup and release, earthquake prediction and selection of VBL sites for margins of the north Pacific

During the past year, the grant supported research on several aspects of crustal deformation. The relation between earthquake displacements and fault dimensions was studied in an effort to find scaling laws that relate static parameters such as slip and stress drop to the dimensions of the rupture. Several implications of the static relations for the dynamic properties of earthquakes such as rupture velocity and dynamic stress drop were proposed. A theoretical basis for earthquake related phenomena associated with slow rupture growth or propagation, such as delayed multiple events, was developed using the stress intensity factor defined in fracture mechanics and experimental evidence from studies of crack growth by stress corrosion. Finally, extensive studies by Japanese geologists have established the offset across numerous faults in Japan over the last one hundred thousand years. These observations of intraplate faulting are being used to establish the spatial variations of the average strain rate of subregions in southern Japan.

Scholz, C. H.↗

A sandwich plate with a part-through and a debonding crack.

The stress analysis of a metal base plate stiffened by a fiber-reinforced composite layer is considered. It is assumed that the two materials are bonded through an adhesive of constant thickness which is treated as a two-dimensional shear spring in the analysis. The metal plate is assumed to contain a through crack of finite length. The composite plate has no flaws. However, due to the high stress concentration around the crack and on the interface, a debonding crack is assumed to exist, encircling the crack in the base plate. The problem is reduced to a pair of integral equations of the second kind with Fredholm-type kernels. By solving these equations the stress intensity factor in the base plate, the boundary of the debonding crack, and the interface shear stresses acting on the adhesive are calculated.

Erdogan, F.↗

Penny-shaped crack in a fiber-reinforced matrix

Using a slender inclusion model developed earlier, the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles, the problem was reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given, and distribution of the stress intensity factor along the crack border was obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Narayanan, T. V.↗

Penny-shaped crack in a fiber-reinforced matrix

Using the slender inclusion model developed earlier the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles the problem is reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given and distribution of the stress intensity factor along the crack border is obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Narayanan, T. V.↗

Finite-element analysis of a weld-penetration problem

The stress concentration factor for a weld penetration defect is calculated by the finite-element method. A stress intensity factor is computed by use of the finite-element solution and the J-integral. The results are compared with experimental results.

Rogge, T. R.↗

Dugdale plastic zone size and CTOD equations for the compact specimen

With the aim of applying the Dugdale model to the compact specimen, the equations for stress intensity factor and crack surface displacement are obtained for a pair of pin loads and a uniform stress acting on a segment of the crack surface. The plastic zone size is calculated from the 'finiteness' condition of Dugdale, and the results agree well with collocation results from Terada (1983). The load that causes incipient yielding at the compression point of the compact specimen is calculated from a finite element strip yield analysis for an elastic-perfectly plastic material. The crack tip opening displacement for the compact specimen is calculated by adding the displacement at the tip of the physical crack length due to the pin load and due to the uniform stress. The results are within 1.5 percent of current collocation results.

Newman, J. C., Jr.↗