Showing papers on "Stress concentration published in 1988"

Mechanisms of fatigue crack propagation in metals, ceramics and composites: Role of crack tip shielding☆

Abstract: Crack tip shielding phenomena, whereby the “effective crack-driving force” actually experienced at the crack tip is locally reduced, are examined with reference to fatigue crack propagation behavior in metals, composites and ceramics. Sources of shielding are briefly described in terms of mechanisms relying on the production of elastically constrained zones which envelop the crack (zone shielding), on the generation of wedging, bridging or sliding forces between the crack surfaces (contact shielding) and on crack path deflection and meandering. Examples are taken from the fatigue behavior of high strength lithium-containing aluminum alloys, aluminum alloy-aramid fiber-epoxy laminate composites, and zirconia ceramics. It is shown that, whereas crack tip shielding can provide a potent means of enhancing “resistance” to crack growth, such extrinsic toughening mechanisms can result in the apparently anomalous behavior of “small cracks” and to the susceptibility of brittle materials to fatigue failure.

The practical use of fracture mechanics

Abstract: 1. Introduction.- 1.1. Fracture control.- 1.2. The two objectives of damage tolerance analysis.- 1.3. Crack growth and fracture.- 1.4. Damage tolerance and fracture mechanics.- 1.5. The need for analysis: purpose of this book.- 1.6. Exercises.- 2. Effects of Cracks and Notches: Collapse.- 2.1. Scope.- 2.2. An interrupted load path.- 2.3. Stress concentration factor.- 2.4. State of stress at a stress concentration.- 2.5. Yielding at a notch.- 2.6. Plastic collapse at a notch.- 2.7. Fracture at notches: brittle behavior.- 2.8. Measurement of collapse strength.- 2.9. Exercises.- 3. Linear Elastic Fracture Mechanics.- 3.1. Scope.- 3.2. Stress at a crack tip.- 3.3. General form of the stress intensity factor.- 3.4. Toughness.- 3.5. Plastic zone and stresses in plane stress and plane strain.- 3.6. Thickness dependence of toughness.- 3.7. Measurement of toughness.- 3.8. Competition with plastic collapse.- 3.9. The energy criterion.- 3.10. The energy release rate.- 3.11. The meaning of the energy criterion.- 3.12. The rise in fracture resistance: redefinition of toughness.- 3.13. Exercises.- 4. Elastic-Plastic Fracture Mechanics.- 4.1. Scope.- 4.2. The energy criterion for plastic fracture.- 4.3. The fracture criterion.- 4.4. The rising fracture energy.- 4.5. The residual strength diagram in EPFM: collapse.- 4.6. The measurement of the toughness in EPFM.- 4.7. The parameters of the stress-strain curve.- 4.8. The h-functions.- 4.9. Accuracy.- 4.10. Historical development of J.- 4.11. Limitations of EPFM.- 4.12. CTOD measurements.- 4.13. Exercises.- 5. Crack Growth Analysis Concepts.- 5.1. Scope.- 5.2. The concept underlying fatigue crack growth.- 5.3. Measurement of the rate function.- 5.4. Rate equations.- 5.5. Constant amplitude crack growth in a structure.- 5.6. Load interaction: Retardation.- 5.7. Retardation models.- 5.8. Crack growth analysis for variable amplitude loading.- 5.9. Parameters affecting fatigue crack growth rates.- 5.10. Stress corrosion cracking.- 5.11. Exercises.- 6. Load Spectra and Stress Histories.- 6.1. Scope.- 6.2. Types of stress histories.- 6.3. Obtaining load spectra.- 6.4. Exceedance diagram.- 6.5. Stress history generation.- 6.6. Clipping.- 6.7. Truncation.- 6.8. Manipulation of stress history.- 6.9. Environmental effects.- 6.10. Standard spectra.- 6.11. Exercises.- 7. Data Interpretation and Use.- 7.1. Scope.- 7.2. Plane strain fracture toughness.- 7.3. Plane stress and transitional toughness, R-curve.- 7.4. Toughness in terms of J and JR.- 7.5. Estimates of toughness.- 7.6. General remarks on fatigue rate data.- 7.7. Fitting the da/dN data.- 7.8. Dealing with scatter in rate data.- 7.9. Accounting for the environmental effect.- 7.10. Obtaining retardation parameters.- 7.11. Exercises.- 8. Geometry Factors.- 8.1. Scope.- 8.2. The reference stress.- 8.3. Compounding.- 8.4. Superposition.- 8.5. A simple method for asymmetric loading cases.- 8.6. Some easy guesses.- 8.7. Simple solutions for holes and stress concentrations.- 8.8. Simple solutions for irregular stress distributions.- 8.9. Finite element analysis.- 8.10. Simple solutions for crack arresters and multiple elements.- 8.11. Geometry factors for elastic-plastic fracture mechanics.- 8.12. Exercises.- 9. Special Subjects.- 9.1. Scope.- 9.2. Behavior of surface flaws and corner cracks.- 9.3. Break through: leak-before-break.- 9.4. Fracture arrest.- 9.5. Multiple elements, multiple cracks, changing geometry.- 9.6. Stop holes, cold worked holes and interference fasteners.- 9.7. Residual stresses in general.- 9.8. Other loading modes: mixed mode loading.- 9.9. Composites.- 9.10. Exercises.- 10. Analysis Procedures.- 10.1. Scope.- 10.2. Ingredients and critical locations.- 10.3. Critical locations and flaw assumptions.- 10.4. LEFM versus EPFM.- 10.5. Residual strength analysis.- 10.6. Use of R-curve and JR-curve.- 10.7. Crack growth analysis.- 10.8. Exercises.- 11. Fracture Control.- 11.1. Scope.- 11.2. Fracture control options.- 11.3. The probability of missing the crack.- 11.4. The physics and statistics of crack detection.- 11.5. Determining the inspection interval.- 11.6. Fracture control plans.- 11.7. Repairs.- 11.8. Statistical aspects.- 11.9. The cost of fracture and fracture control.- 11.10. Exercises.- 12. Damage Tolerance Substantiation.- 12.1. Scope.- 12.2. Objectives.- 12.3. Analysis and damage tolerance substantiation.- 12.4. Options to improve damage tolerance.- 12.5. Aircraft damage tolerance requirements.- 12.6. Other requirements.- 12.7. Flaw assumptions.- 12.8. Sources of error and safety factors.- 12.9. Misconceptions.- 12.10. Outlook.- 12.11. Exercises.- 13. After the Fact: Fracture Mechanics and Failure Analysis.- 13.1. Scope.- 13.2. The cause of service fractures.- 13.3. Fractography.- 13.4. Features of use in fracture mechanics analysis.- 13.5. Use of fracture mechanics.- 13.6. Possible actions based on failure analysis.- 13.7. Exercises.- 14. Applications.- 14.1. Scope.- 14.2. Storage tank (fictitious example).- 14.3. Fracture arrest in ships.- 14.4. Piping in chemical plant (fictitious example).- 14.5. Fatigue cracks in railroad rails.- 14.6. Underwater pipeline.- 14.7. Closure.- 15. Solutions To Exercises.

A Theory of Particle-Reinforced Plasticity

Abstract: A simple, albeit approximate, theory is developed to determine the elastoplastic behavior of particle-reinforced materials. The elastic, spherical particles are uniformly dispersed in the ductile, work-hardening matrix. The method proposed combines Mori-Tanaka’s concept of average stress in elasticity and Hill’s discovery of a decreasing constraint power of the matrix in polycrystal plasticity. Under a monotonic, proportional loading the latter was characterized, approximately, by the secant moduli of the matrix. The theory is established for both traction and displacement-prescribed boundary conditions, under which, the average stress and strain of the constituents and the effective secant moduli of the composite are explicitly given in terms of the secant moduli of the matrix and the volume fraction of particles. In particular, the yield stress and work-hardening modulus of the composite are shown to be inversely proportional to the deviatoric part of average stress concentration factors of the matrix, and therefore will increase (or decrease) with increasing hard (or soft) particle concentration. It is also found that, even if the matrix is plastically incompressible, the composite as a whole is not. Comparison between the theory and the experiment for a silica/epoxy system shows a reasonable agreement. The theory is also compared with a recently developed one by Arsenault and Taya; while both give the same initial yield stress for the composite, the work-hardening modulus predicted by their theory is found to be higher.

Can natural faults propagate under Mode II conditions

Abstract: Various brittle geological structures form from the tip of preexisting joints. Experiments have been carried out to investigate their mechanical origin and to find out whether a planar defect can propagate in its ownplane under mode II geometrical conditions (displacement parallel to the defect plane and perpendicular to the edge) as supposed by the classical rupture mechanics model, and in particular, whether mode II can be an elementary fracture mechanism, which is not clear in the model and has not been experimentally demonstrated. A biaxial loading device (plane strain) allowed direct observation of fracture propagation from an angled slot in plates of Polymethylmethacrylate (PMMA, Altuglas) and sandstone (low and high porosity). Under uniaxial load, mode I propagation of the classical branch fracture occurred in both materials, but its development was inhibited under biaxial loading (low σ3/σ1 ratio). At higher stress/strain levels, shear zones (clearly distinguishable from the branch fracture) developed from the slot tip. In PMMA they consisted of the prograding development of en echelon shallow microcracks formed in mode I and more or less associated with plastic deformation. In sandstone a narrow shear zone propagated in the prolongation of the defect (slowly in the high-porosity samples and abruptly in the low-porosity ones) accompanied by conjugate shear fractures. The deformation mechanism was cataclasis, implying tensile (mode I) microfractures. These experiments suggest that mode II cannot exist as an elementary (primary) fracture mechanism but can only be a macroscopic fracture phenomenon which must necessarily involve tensile (mode I) microcrack formation. The latter is linked to stress concentrations in the prolongation of the existing joint. As such mode II initiated shear zones have not been generated in glass, a high density of small defects which can be mobilized under shear stress would seem essential. These ideas can be used to interpret some types of natural faults.

Plate separation and anchorage of reinforced concrete beams strengthened by epoxy-bonded steel plates

Abstract: This paper deals with the problem of Anchorage at the ends of steel plates glued to the tensile faces of reinforced concrete beams. A simple theoretical study of the force systems at the plate/glue and the glued concrete interfaces is presented. This suggests that high stress concentrations and peeling forces are present at the ends of the plates when the composite beam is loaded in flexure. Tests carried out to investigate the effectiveness of different Anchorage arrangements are described in detail. The results from these tests confirm that, at the ends of the plates, interface stress concentrations exist, which have limiting peak values in the region of root 2 x tensile splitting strength of the concrete. Theoretical interface bond stresses, based on simple elastic behaviour, are found to have no consistent relationship to the measured peak values. However, if the maximum (unreduced) plate thickness is always used in these calculations, a simple method is proposed for obtaining a reasonable assessment of the peak stress. The efficiency of the different Anchorage details is discussed, and it is shown that the use of additional glued anchor plates gives the best results. These plates overcome the problem of Anchorage failure and enable the full theoretical flexural strength to be achieved, together with ductile behaviour.(a)

Short and long fatigue crack growth: A unified model

Abstract: In this model the growth of a crack is analysed in terms of the successive blocking of the plastic zone by slip barriers (e.g. grain boundaries) and the subsequent initiation of the slip in the next grain. The discontinuous character of the slip process (slip jumps) plays a fundamental role in the model. The factor governing the transfer of slip across a grain boundary is considered to be the stress concentration ahead of the plastic zone which, for a constant applied stress τ, is found to be dependent only on a parameter n = a/c defining the position of the crack tip relative to the grain boundary. The discrete behaviour of the slip has a strong influence in the short-crack period and hence cannot be neglected in the analysis of the crack growth rate. This period is characterized by large variations in the parameter n. In the long-crack period the slip jumps do not influence the overall description of the growth and the parameter n is almost constant. By making the crack extension per cycle prop...

Quantitative Evaluation of Effects of Nonmetallic Inclusions on Fatigue Strength of High Strength Steel

Abstract: First, the effects of nonmetallic inclusions on the fatique strength of metals are reviewed and the influential factors are revealed. Next, it is emphasized that the effects of nonmetallic inclusions must be analyzed from the viewpoint of small defects or small cracks, because the threshold condition at the fatigue limit is not the condition for crack initiation but the condition for the non-propagation of a crack emanating from defects or inclusions. Finally. from this point of view, the equation for the prediction of the threshold stress intensity factor range ΔKth and fatigue limit σw for defects and small cracks was applied to predict those for inclusions contained in high strength steels. It is demonstrated that the square root of the projected area of inclusions and the Hv of the matrix are the crucial parameters to predict the fatigue limit of metals containing inclusions. The predictions by the proposed equations were in very good agreement with the experimental results obtained from the fracture surface showing fish-eye patterns. The reasons why the fatigue limit σw of high strength steels does not increase linearly with increasing hardness, and why the scatters of fatigue limit are so large are made clear.

Mechanics of Fatigue Crack Closure

Abstract: Papers are presented on plasticity induced crack closure, crack closure in fatigue crack growth, the dependence of crack closure on fatigue loading variables, and a procedure for standardizing crack closure levels. Also considered are a statistical approach to crack closure determination, the crack closure behavior of surface cracks under pure bending, closure measurements on short fatigue cracks, and crack closure under plane strain conditions. Other topics include fatigue crack closure behavior at high stress ratios, the use of acoustic waves for the characterization of closed fatigue cracks, and the influence of fatigue crack wake length and state of stress on crack closure.

Composite technology for total hip arthroplasty.

Abstract: Composite materials, which can be very strong while having a low modulus of elasticity, are being studied because such materials have potential to be made into isoelastic hip prostheses. Composites intended for medical applications incorporate carbon or polyamide as a fiber component, while polysulfone, polyetheretherketone, or polyethylene is used as a matrix component. Mechanical properties (especially the modulus of elasticity) are emphasized because of the desire to match those properties of the proximal femur. Many of the variables that affect the mechanical properties of these materials are explained. The application of stress to different fiber orientations demonstrates the mechanical properties of the composite, and this is proved mathematically. It is shown that in composites with fibers oriented in the same direction, the modulus of elasticity in the direction of the fibers generally approaches that of the fibers as the amount of matrix decreases. Perpendicular to the fibers, the modulus of elasticity of the composite is only slightly greater than that of the matrix material. For isotropic chopped-fiber composites, the modulus of elasticity approaches that of the matrix as the fiber content decreases; at high-fiber content, the modulus is significantly less than that of oriented long-fiber composites. In general, the modulus of elasticity and fiber content have a linear relationship. Composites have fatigue properties that vary with direction and approach ultimate strength in tension but are lower in compression. The fatigue properties of proposed composites are discussed. Abrasion as a cause of stress concentration sites and wear particles is considered.

Rupture Initiation in Shear Fracture of Rocks' An Experimental Study

Abstract: We used a torsional geometry to grow shear ruptures in two fine-grained rock types. The sample has a slot that is loaded to produce a strong mode 3 shear stress concentration. The onset and growth of the damage zone is detected by monitoring the elastic stiffness of the samples. We find that the samples continue to harden after the onset of fracture. This is initially accompanied by oblique tensile cracks forming at the stress concentration. The peak in supported load apparently corresponds to the onset of strain localization, with the development of cross-cutting shear fractures. We attempted to estimate the partitioning of energy dissipation between elastic and frictional components with a fracture mechanics analysis. The elastic energy increases with normal stress, but scatter in the inelastic data does not allow identification of convincing trends. The sample is too small to develop a complete transition to a shear rupture. The geometry of the fractures is used to explain the energy relations as well as other experimental observations

Fracture Mechanics of Unidirectional Composites Using the Shear-Lag Model I: Theory

Abstract: Using the shear-lag model, we have solved for the crack-tip stress concentrations in double-edge notch and center notch unidirectional composites of finite width From the stress-state solution, expressions are derived for strain energy release rate due to crack propagation through the fibers and due to crack propagation parallel to the fibers It is pro posed that these new equations, which include geometric correction factors, may be used for fracture mechanics analyses of unidirectional composites and that their use will pro vide better physical insight into composite fracture Because the heterogeneous nature of composites is specifically taken into account, it is suggested that these new equations are superior to ones derived from classical fracture mechanics or from stress-state solutions for homogeneous materials

Effects of SiC reinforcement and aging treatment on fatigue crack growth in an AlSiC composite

Abstract: The effects of SiC reinforcement and matrix aging treatment on fatigue crack growth behavior in a powder metallurgy aluminum 2124 alloy-SiC whisker composite were investigated. The microstructures were designed such that the matrix of the composite material and the unreinforced control aluminum alloy 2124 with an identical processing history had similar hardness and precipitation characteristics. The threshold stress intensity factor range ΔK0 for tensile fatigue crack growth was obtained using a procedure whereby mode I precracks were initiated in uniaxial cyclic compression prior to tension fatigue. The composite exhibits a ΔK0 value which is about twice that of the control alloy. However, ΔK0 is relatively insensitive to variations in both the aging treatment and the mean stress of the fatigue cycle in both the composite and the control alloy. Possible mechanisms underlying this trend are discussed.

The effect of fiber-matrix stress transfer on the strength of fiber-reinforced composite materials

Abstract: A model for the mechanism of tensile failure in oriented fiber composites based on random fragmentation of the reinforcing fibers biased by stress concentrations at fracture sites has been developed. Single-fiber composites and composite strands of 34 to 36 volume percent fiber were prepared from an epoxy resin reinforced with Hercules AS4, HMS4, and IM6G carbon fibers. Fiber strength distributions and single-fiber composite fragmentation data were used to calculate theoretical composite tensile strengths, which were then compared with experimental values. The fractures in single-fiber composites were observed in situ under cross-polarized light, and the mechanisms of interfacial failure were discussed.

A simplified laboratory approach for the prediction of short crack behavior in engineering structures

Abstract: — Conventionally determined fatigue threshold information (ASTM E647) can lead to non-conservative estimates of fatigue lifetimes when these data are utilized in damage tolerant design assessments. The non-conservative nature of such data can be attributed primarily to the development of excessively large amounts of crack closure at low R-ratios, particularly at near threshold stress intensity factor levels. These high closure levels attenuate the effective stress intensity condition prevailing at the crack tip and confound attempts to predict the behavior of short cracks that exhibit limited crack closure. A modified test procedure, involving constant maximum stress intensity factor (Kcmax) test conditions, is described which identifies fatigue crack propagation (FCP) threshold behavior in the absence of detectable amounts of crack closure. These data have been generated with conventional long crack specimens for several aluminum, iron, and nickel-based alloys and which are shown to closely simulate the FCP response of short cracks in these engineering materials. As such, the modified threshold test procedure, incorporating constant Kmax loading conditions, represents a valuable tool in the prediction of the cyclic lifetime of engineering components. The stress-cyclic lifetime (S-N) curve for aluminum butt-welded beams was computed based on Kcmax data and found to be in excellent agreement with actual test results.

Computation of the amplitude of stress singular terms for cracks and reentrant corners

Abstract: : The theoretical basis and performance characteristics of two new methods for the computation of the coefficients of the terms of asymptotic expansions at reentrant corners from finite element solutions are presented The methods, called the contour integral method and the cutoff function method, are very efficient: The coefficients converge to their true values as fast as the strain energy, or faster In order to make the presentation as simple as possible, we assume that the elastic body is homogeneous and isotropic, is loaded by boundary tractions only and, in the neighborhood of the reentrant corner, its boundaries are stress free The methods described herein can be adapted to cases without such restrictions Keywords: Finite element methods, P-extension, Fracture mechanics, Elasticity, Stress intensity factors, Mixed mode, Extraction methods, Convergence, Error estimate

Influence of Stress State on Crack Growth Retardation

Abstract: Several mechanisms have been proposed in the literature to account for crack growth retardation following a single peak overload. In order to determine the dominant mechanism, overload tests were performed on thick and thin specimens made from BS4360 50B structural steel. The baseline stress intensity range was 25 MPa √m and the load ratio (= minimum load/maximum load of fatigue cycle) was 0.05, while the overload was of stress intensity range 50 MPa √m. It was observed that the crack growth and closure responses were different at the surface and in the bulk of the thick specimen; no such variations in behavior occurred along the crack front for the thin specimen. For both thicknesses of material, the crack growth rate predicted by measurements of the crack opening load was in agreement with the observed crack growth rate, except for the period when crack growth rates were recovering from the slowest transient growth rate to the post-overload stabilized value. This discrepancy was due to the phenomenon of discontinuous closure-the crack first closed at a location far from its tip. Fracture surface profiles showed that the crack path deviated by only a small amount after application of the overload; hence the retarded growth cannot be due to crack branching. It is concluded from these tests and from a critical examination of the literature that, at high baseline AK levels, retardation is due to plasticity-induced crack closure. At low baseline AK levels approaching the threshold value, retardation may be due to plasticity-induced crack closure or to irregularities of the crack front.

Fatigue crack propagation in aluminum-lithium alloy 2090: Part II. small crack behavior

Abstract: A study has been made of the mechanics and mechanisms of fatigue crack propagation in a commercial plate of aluminum-lithium alloy 2090-T8E41. In Part I, the crack growth and crack shielding behavior of long (≳5 mm) through-thickness cracks is examined as a function of plate orientation and load ratio, and results compared to traditional high strength aluminum alloys. It is shown that rates of fatigue crack extension in 2090 are, in general, significantly slower (at a given stress intensity range) than in traditional alloys, although behavior is strongly anisotropic. Differences in growth rates of up to 4 orders of magnitude are observed between the L-T, T-L, and T-S orientations, which show the best crack growth resistance, and the S-L, S-T, and L + 45, which show the worst. Such behavior is attributed to the development of significant crack tip shielding (i.e., a reduction in local crack driving force), primarily resulting from the role of the crack path morphology in inducing crack deflection and crack closure from the consequent asperity wedging. Whereas crack advance perpendicular to the rolling plane (e.g., L-T,etc.) involves marked crack path deflection and branching, thereby promoting very high levels of shielding to cause the slowest growth rates, fatigue fractures parallel to the rolling plane (e.g., S-L,etc.) occur by an intergranular, delamination-type separation, with much lower shielding levels to give the fastest growth rates. The implications of such “extrinsic toughening” effects on the fracture and fatigue properties of aluminum-lithium alloys are discussed in detail.

Fatigue crack growth from indentation flaw in ceramics

Abstract: The indentation crack has been used as a model of surface flaw in the strength tests of ceramics. In evaluation of such strength properties, some attention should be paid to the residual stress effect due to indentation. In this study, fatigue crack growth behavior from indentation flaws was investigated in sintered silicon nitride and alumina. In both materials, a V-shaped behavior was observed in the relation between the maximum stress intensity factor and the crack growth rate. The indentation crack was analyzed using fracture mechanics procedure to take account of the residual component. On the basis of the analysis, an effective stress intensity factor for crack growth was successfully evaluated. The growth rate was correlated to the effective stress intensity factor, and the relation was found to be approximated by a power law equation. The fatigue crack growth property obtained as above was applied to an estimation of fatigue life of specimens without artificial flaws. The flaw size effect was also discussed based on the result.