Experimental determination ofK I for surface cracks in a square tube under torsion

This research used the fatigue-crack-growth-rate experimental method to obtainK _I for initial semi-elliptical 45-deg inclined, longitudinal and transverse surface cracks in a hollow square tube subjected to pure torsion. Both side and corner surface cracks were investigated. Reference crack-growth-rate data using CT and SEN specimens taken from the mild-steel tubes were used in calculations. All cracks propagated in mode I on the surface at 45 deg to the longitudinal axis in the plane of the maximum tensile stress. Mixed-mode crack growth occurred subsurface for the longitudinal and transverse cracks. The experimental results were compared with other semi-elliptical surface crackK _I solutions.     

CTOA and crack-tunneling measurements in thin sheet 2024-T3 aluminum alloy

The stable tearing behavior of 2.3-mm thick sheets of 2024-T3 aluminum alloy was experimentally investigated for middle crack tension specimens having initial flaws that were: (a) flat fatigue cracks (low fatigue stress) and (b) 45-deg through-thickness slant cracks (high fatigue stress). The critical CTOA values during stable tearing were measured by two independent methods, optical microscopy and digital-image correlation. Results from the two methods agree well.The CTOA measurements and observations of the fracture surfaces have shown that the initial stable tearing behavior of low and high fatigue stress tests is significantly different. The cracks in the low fatigue stress tests underwent a transition from flat-to-slant crack growth, during which the CTOA values were high and significant crack tunneling occurred. After crack growth equal to about the thickness (a>B), CTOA reached a constant value of 6 deg and after crack growth equal to about twice the thickness (a>2B), crack tunneling stabilized. The cracks in the high fatigue stress tests reach the same constant CTOA value after crack growth equal to about the thickness, but produced only slightly higher CTOA values during initial crack growth. The amount of tunneling in the high fatigue stress tests was about the same as that in the low fatigue stress tests after the flat-to-slant transition.This study indicates that stress history has an influence on the initial portion of the stable tearing behavior. The initial high CTOA values, in the low fatigue crack tests, coincided with large three-dimensional crack front shape changes due to a variation in the through-thickness crack-tip constraint. The measured CTOA reached a constant value of 6 deg for crack growth of about the specimen thickness. This coincided with the onset of 45-deg slant crack growth and a stabilized, slightly tunneled (about 20 percent of the thickness) crack-front shape. For crack growth on the 45-deg slant, the crack front and local field variables are still highly three dimensional.     

Mode III fracture behavior of laminated composite with edge crack in torsion

A three-dimensional (3-D) finite element analysis was performed on a [90,(+45/−45)_n,(−45/+45)_n,90]_s class of laminated composites under the edge crack torsion (ECT) test configuration. Finite element delamination models were established and formulas for calculating the Mode III fracture toughness from 3-D finite element models were developed. The relations between the interlaminar fracture behavior and various configuration parameters were investigated and the effects of point loads, ends, geometry, Mode II interference, and friction were evaluated. Results showed that with proper selection of ECT specimen configuration and layup, the delamination could grow in pure Mode III in the middle region of the specimen. Specimen end effect played an important role in the ECT test. A Mode II component occurred in the end regions but it did not interfere significantly with the Mode III delamination state. Specimen dimension ratio, layup, and crack length exhibited significant effect on the interlaminar fracture behavior and the calculated strain energy release rates. However, friction between crackfaces was found to have negligible effect on the interlaminar properties.     

Effect of temperature on the fracture modes of BHW-35 steel under mode-II loading

Finite element method (FEM) has been used to analyze the stress and strain fields and the stress tri-axial levels around the tip of the crack under mode- II loading. The results show that: under mode- II loading, the direction of the maximum tensile stress and that of the maximum tri-axial levels (R _o ) exist at an angle of –75. 3° from the original crack plane; the maximum shear stress andR _o = 0 exist along the original crack plane.Mode- II loading experiment using BHW-35 steel at different temperatures show that there are two kinds of fracture mode, opening mode (or tensile mode) and sliding mode (or shear mode). A decrease in temperature causes the fracture mode to change from shear mode to tensile mode. For BHW-35 steel, this critical temperature is about –90 C. Actually, under any kind of loading mode (mode I . mode II , mode III or mixed mode), there always exist several kinds of potenital fracture modes (for example, opening mode, sliding mode, tearing mode or mixed mode). The effect of temperature under mode- II loading is actually related to the change of the elastic-plastic properties of the material.     

Biaxial testing of [O2/±45] s graphite/epoxy plates with holes

An experimental investigation was conducted to study the behavior under biaxial-tensile loading of [O₂/±45] _s graphite/epoxy plates with circular holes and to determine the influence of hole diameter on failure. The specimens were 40-cm×40-cm (16-in.×16-in.) graphite/epoxy plates of [O₂/±45] _s layup. Four hole diameters, 2.54 cm (1.00 in.), 1.91 cm (0.75 in.), 1.27 cm (0.50 in.) and 0.64 cm (0.25 in.), were investigated. Deformations and strains were measured using strain gages and birefringent coatings. Biaxial tension in a 2∶1 ratio was applied by means of four whiffle-tree grip linkages and controlled with a servohydraulic system. Stress and strain redistributions occur around the hole at a stress level corresponding to localized failure around the 67.5-deg location and nonlinear strain response at the 0-deg location. Maximum measured strains at failure on the hole boundary are higher (approximately 0.016) than the highest ultimate strain of the unnotched laminate (0.010). Two basic patterns of failure were observed: (a) horizontal cracking initiating at points off the horizontal axis and accompanied by extensive delamination of the subsurface ±45 deg plies, and (b) vertical cracking along vertical tangents to the hole and accompanied by delamination of the outer 0-deg plies. The strength reduction ratios are lower than corresponding values for uniaxial loading by approximately 16 percent, although the stress-concentration factor under biaxial loading is lower.     

Experimental investigation on the propagation of fatigue cracks emanating from sharp notches

The effect of notch geometry on the propagation of fatigue cracks emanating from sharp V-shaped notches is investigated by means of an experimental campaign performed on Al-7075-T651 specimens carrying notches with opening angles of 45°, 90°, and 135°. The samples were tested using a servohydraulic machine under different loading directions and at several loading levels. The crack deflection induced by the variation in loading direction was determined my measuring the kinking angle and by studying the crack propagation plane through fractographic analysis. A linear elastic fracture mechanics approach was adopted for the analysis of experimental results. Stress intensity factors were calculated using an appropriate weight function set up for studying inclined edge cracks emanating from sharp V-notches. The influence of K _II on the crack propagation was discussed on the basis of theoretical and semi empirical models.     

Path-independent integrals for the direct determination of stress intensity factors in certain classical crack problems

Stress intensity factors have been determine directly for certain special crack problems with the help of J or other path-independent integrals. Such procedures have not been used successfully in what are perhaps the most classical of all crack problems: those in two dimensions involving a crack of finite length in an infinite medium with loading at infinity of either Mode I, Mode II or Mode III type. We give a new class of path-independent integrals which are suitable for this purpose.     

π平面上原状土的空心扭剪试验

为了通过空心扭剪试验获得原状土在π 平面上的屈服特性,在分析空心扭剪试验仪加载过程和加载特点的基础上,研究了空心圆柱试样可实现的应力状态,并设计了相应的加载路径．与重塑试样不同,原状土样的初始应力状态位于K0 固结线上而不是等倾线上,因此,其加载路径应从原点开始沿K0 固结线行至原始应力状态,然后再在π 平面上进行以初始应力为起点的等p 试验．在考虑原状土的初始应力状态和各项异性的基础上,针对具有不同主应力方向角的平行试样,给出了等p 条件下保持主应力方向角不变的加载路径实现方法,采用该方法可得到任意平均主应力时π 平面上六分之一范围内的屈服曲线,该范围对应于大主应力方向角从-45o~45o．本文设计的加载方案可完成真三轴试验的部分功能,但经济成本相对较低,操作方法简单易行．     

Photoelastic study of the stresses near a cleavage crack

Photoelastic analysis has been used to determine the stress distribution near the tip of a cleavage crack. The crack bisects a slender rectangular bar along its length, and forces are applied at one end of it tending to open it out. The region of high stresses is localized in a region of the order of the half-width of the bar in size. Very near the crack tip, the stresses decrease in proportion to the inverse square root of the distance from the crack tip. The maximum gradient of the principal tensile stress lies at an angle of 70 to 80 deg from the plane of the crack. Contour maps of the principal stresses, the 45-deg shear stress and the maximum tensile stress are presented.     

Anisotropic plastic stress fields at a slowly propagating crack tip

Under the condition that any perfectly plastic stress components at a crack tip are nothing but the functions of 0 only making use of equilibrium equations. Hill anisotropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastic stress fields at the slowly steady propagating tips of plane and anti-plane strain. Applying these general analytical expressions to the concrete cracks, the analytical expressions of anisotropic plastic stress fields at the-slowly steady propagating tips of Mode I and Mode III cracks are obtained. For the isotropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfectly plastic stress fields.     

Finite plane and anti-plane elastostatic fields with discontinuous deformation gradients near the tip of a crack

In this paper the fully nonlinear theory of finite deformations of an elastic solid is used to study the elastostatic field near the tip of a crack. The special elastic materials considered are such that the differential equations governing the equilibrium fields may lose ellipticity in the presence of sufficiently severe strains.The first problem considered involves finite anti-plane shear (Mode III) deformations of a cracked incompressible solid. The analysis is based on a direct asymptotic method, in contrast to earlier approaches which have depended on hodograph procedures.The second problem treated is that of plane strain of a compressible solid containing a crack under tensile (Mode I) loading conditions. The materials is characterized by the so-called Blatz-Ko elastic potential. Again, the analysis involves only direct local considerations.for both the Mode III and Mode I problems, the loss of equilibrium ellipticity results in the appearance of curves (elastostatic shocks) issuing from the crack-tip across which displacement gradients and stresses are discontinuous.The results communicated in this paper were obtained in the course of an investigation supported by Contract N00014-75-C-0196 with the Office of Naval Research.     

A viscoplastic study of crack-tip deformation and crack growth in a nickel-based superalloy at elevated temperature

Viscoplastic crack-tip deformation behaviour in a nickel-based superalloy at elevated temperature has been studied for both stationary and growing cracks in a compact tension (CT) specimen using the finite element method. The material behaviour was described by a unified viscoplastic constitutive model with non-linear kinematic and isotropic hardening rules, and implemented in the finite element software ABAQUS via a user-defined material subroutine (UMAT). Finite element analyses for stationary cracks showed distinctive strain ratchetting behaviour near the crack tip at selected load ratios, leading to progressive accumulation of tensile strain normal to the crack-growth plane. Results also showed that low frequencies and superimposed hold periods at peak loads significantly enhanced strain accumulation at crack tip. Finite element simulation of crack growth was carried out under a constant ΔK-controlled loading condition, again ratchetting was observed ahead of the crack tip, similar to that for stationary cracks.A crack-growth criterion based on strain accumulation is proposed where a crack is assumed to grow when the accumulated strain ahead of the crack tip reaches a critical value over a characteristic distance. The criterion has been utilized in the prediction of crack-growth rates in a CT specimen at selected loading ranges, frequencies and dwell periods, and the predictions were compared with the experimental results.     

Effects of fatigue and environment on residual strengths of center-cracked graphite/epoxy buffer strip panels

Graphite/epoxy buffer strip panels were subjected to a fatigue loading spectrum, moisture conditioning, or heating and then statically tested in tension to determine their residual strengths. The specimens were made with T300/5208 graphite/epoxy in a 16-ply quasi-isotropic layup, [45/0/ - 45/90]_2s, with two different buffer strip materials: Kevlar-49 or S-glass. Each panel was cut in the center to represent damage.The panels made from each buffer strip material were divided into two test conditions: those panels tested at room temperature and those tested at 82°C. Each test condition was further divided into two groups, panels tested at ambient conditions and panels tested after moisture conditioning. Thus, there were four combinations of preconditioning and test condition: (1) ambient condition tested at room temperature, (2) moisture conditioned tested at room temperature, (3) ambient condition tested at 80°C, and (4) moisture conditioned tested at 82°C. After preconditioning and fatigue loading, all specimens were statically loaded in tension to failure to determine their residual strengths.After fatigue loading, the buffer strips arrested the crack growth and increased the residual strengths significantly over those of plain laminates without buffer strips under all conditions, with one exception. For the S-glass buffer strip panels with moisture conditioning, the buffer strip arrested the crack growth, but the residual strength was increased only slightly over the strength of a plain laminate. The stiffness of the panels was not affected by the fatigue cycling. Repeated fatigue cycling did not produce any damage growth at the crack tips.Paper was presented at the 1988 SEM Spring Conference on Experimental Mechanics held in Portland, OR on June 5–10.     

Intrinsic coupling of near-tip matrix crack formation to mode III delamination advance in laminated polymeric matrix composites

Laminated carbon/epoxy specimens are loaded in anti-plane shear to investigate the relationship between near-tip matrix crack formation and the apparent mode III delamination toughness. Specimens are tested with different insert lengths to various load levels and examined fractographically. Near-tip matrix cracks are found to initiate and propagate intralaminarly before the onset of planar growth. These cracks are inclined at approximately 45° to the delamination plane and are perpendicular to the direction of maximum near-tip tensile stress. It is found that this represents an intrinsically coupled sequence of events for anti-plane shear loading of continuous fiber laminated polymeric composites when a preexisting delamination is bounded by plies that have their fiber direction aligned with the direction of macroscopic advance. This sequence of events violates the assumptions used in the reduction of data from common mode III tests. It therefore invalidates the associated toughness measurements, and may account for or strongly contribute to the common observation that laminated polymeric composites exhibit an apparent mode III delamination toughness that is dependent on test geometry.     

A theoretical investigation on the vibrational characteristics and torsional dynamic response of circumferentially cracked turbo-generator shafts

Turbo-generator shafts are often subjected to complex dynamic torsional loadings, resulting in generation and propagation of circumferential cracks. Mode III fatigue crack growth generally results in a fracture surface consisting of peaks and valleys, resembling a factory roof. The fracture surface roughness depends on the material microstructure, the material yield strength, and the applied cyclic torque amplitude. This crack pattern can severely affect the vibration characteristics of the shafts. The accurate evaluation of the torsional dynamic response of the turbo-generator shafts entails considering the local sources of energy loss in the crack vicinity. The two most common sources of the energy loss are the local energy loss due to the plasticity at the crack tip and frictional energy loss due to interaction of mutual crack surfaces. A theoretical procedure for evaluating the values of the system loss factors corresponding to these sources of energy loss is presented. Furthermore, the local flexibility is obtained by evaluating the resistance of the cracked section of the shaft to the rotational displacement. The shaft material is assumed to be elastic perfectly plastic. The effects of the applied Mode III stress intensity factor and the crack surface pattern parameters on the energy loss due to the friction and the energy loss due to the plasticity at the crack tip are investigated. The results show that depending on the amplitude of the applied Mode III stress intensity factor, one of these energy losses may dominate the total energy loss in the circumferentially cracked shaft. The results further indicate that the torsional dynamic response of the turbo-generator shaft is significantly affected by considering these two sources of the local energy loss.     

The influence of errors in an interferogram analysis

In determining the influence of random errors in experimental measurement and data reduction, calculus may be applied to some problems where compounded error effects are encountered. However, for some processes it may be more convenient to apply a method of analysis described here which is based on computer simulation of errors, a variation of the so-called Monte Carlo technique. Interferometric moiré fringe patterns corresponding to in-plane displacement fields at 0, 45 and 90 deg, to the plane of the crack, taken from compact tension specimens, were analyzed to evaluate theJ-integral fracture parameter. Since theJ value for each load point was derived from over 100 separate measurements of fringe spacings, each with a significant probability of error, and it was desired to establish the magnitude of these errors on the final outcome, a Monte Carlo simulation of the analysis errors was performed. As a result of the simulation exercise, it could be concluded that the level of errors generated in the fringe-analysis procedure did not significantly affect the value ofJ obtained.     

The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials

This investigation is concerned with the deformations and stresses in a slab of all-around infinite extent containing a traction-free plane crack, under conditions of plane strain. The analysis is carried out within the framework of the fully nonlinear equilibrium theory of homogeneous and isotropic incompressible elastic solids. For a fairly wide class of such materials and general loading conditions at infinity, assymptotic estimates appropriate to the various field quantities near the crack-tips are deduced. For a subclass of the materials considered, these results — in contrast to the analogous predictions of the linearized theory — lead to the conclusion that the crack opens up in the neighborhood of its tips even if the applied loading is antisymmetric about the plane of the crack, (e.g., Mode II loading). It is shown further that the non-linear global crack problem corresponding to such a loading in general cannot admit an antisymmetric solution.The results communicated in this paper were obtained in the course of an investigation supported in part by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.     

Influence of residual stresses on the tensile strength of composite-metal sandwich laminates

The tensile strength of boron-epoxy/aluminum sandwich laminates is discussed relative to the residual thermal stresses which are present as a result of curing and bonding at an elevated temperature. It is shown that the sandwich laminates investigated in this study exhibit three distinct modes of failure depending upon the fiber orientation of the composite. Sandwich laminates with moderate-to-high percentage of 0-deg fibers exhibit early failures initiated by edge effect; laminates with moderate to high percentage of 90-deg fibers fail according to a first-ply failure criterion; laminates with moderate-to-high percentages of ±45 deg plies fail at strains equal to or greater than the failure strain of the corresponding all-composite laminate.     

A novel method in determination of dynamic fracture toughness under mixed mode I/II impact loading

The objective of this paper is to propose a novel methodology for determining dynamic fracture toughness (DFT) of materials under mixed mode I/II impact loading. Previous experimental investigations on mixed mode fracture have been largely limited to qusi-static conditions, due to difficulties in the generation of mixed mode dynamic loading and the precise control of mode mixity at crack tip, in absence of sophisticated experimental techniques. In this study, a hybrid experimental–numerical approach is employed to measure mixed mode DFT of 40Cr high strength steel, with the aid of the split Hopkinson tension bar (SHTB) apparatus and finite element analysis (FEA). A fixture device and a series of tensile specimens with an inclined center crack are designed for the tests to generate the components of mode I and mode II dynamic stress intensity factors (DSIF). Through the change of the crack inclination angle β (=90°, 60°, 45°, and 30°), the K_II/K_I ratio is successfully controlled in the range from 0 to 1.14. A mixed mode I/II dynamic fracture plane, which can also exhibit the information of crack inclination angle and loading rate at the same time, is obtained based on the experimental results. A safety zone is determined in this plane according to the characteristic line. Through observation of the fracture surfaces, different fracture mechanisms are found for pure mode I and mixed mode fractures.     

Subcritical and fatigue crack growth in anti-plane strain state

Assuming elastic-plastic material behavior the slow growth of Mode III crack under both monotonic and pulsating loadings is considered. Rice's idea of universal R-curve is employed while the mathematical analysis is based on the one-dimensional plasticity model suggested by Kostrov and Nikitin. Motion of a quasi-static Mode III crack is studied and the stable/unstable transition points are found through application of the final stretch failure condition proposed in 1972 by Wnuk. A logarithmic formula for fatigue crack extension rate is derived. Results are compared to other well-known solutions.