Showing papers on "Fracture mechanics published in 1992"

The relation between crack growth resistance and fracture process parameters in elastic-plastic solids

Abstract: CKA~K growth initiation and subsequent resistance is computed for an elastic-plastic solid with an idealized traction separation law specified on the crack plane to characterize the fracture process. The solid is specified by its Young’s modulus, E, Poisson’s ratio, v, initial tensile yield stress, (or, and strain hardening exponent, N. The primary parameters specifying the traction-separation law of the fracture process are the work of separation per unit area, To. and the peak traction, 6. Highly refined calculations have been carried out for resistance curves. K,(Arr), for plane strain, mode I growth in small-scale yielding as dependent on the parameters characterizing the elastic-plastic properties of the solid and its fracture process. With K,, = [El-,/( I ~ v’)] ’ 2 as the intensity needed to advance the crack in the absence ofplasticity, K,J& is presented in terms of its dependence on the two most important parameters, d/nr and N, with special emphasis on initiation toughness and steady-state toughness, Three applications of the results are made : to predict toughnesss when the fracture process is void growth and coalescence, to predict the role of plasticity on interface toughness for similar materials bonded together, and to illuminate the role of plasticity in enhancing toughness in dual-phase solids. The regime of applicability of the present model to ductile fracture due to void growth and coalescence, wherein multiple voids interact within the fracture process zone, is complementary to the regime of applicability of models describing the interaction between a single void and the crack tip. The two mechanism regimes are delineated and the consequence of a transition between them is discussed.

Fracture mechanics for piezoelectric ceramics

Abstract: We Study cracks either in piezoelectrics, or on interfaces between piezoelectrics and other materials such as metal electrodes or polymer matrices. The projected applications include ferroelectric actuators operating statically or cyclically, over the major portion of the samples, in the linear regime of the constitutive curve, but the elevated field around defects causes the materials to undergo hysteresis locally. The fracture mechanics viewpoint is adopted—that is, except for a region localized at the crack tip, the materials are taken to be linearly piezoelectric. The problem thus breaks into two subproblems: (i) determining the macroscopic field regarding the crack tip as a physically structureless point, and (ii) considering the hysteresis and other irreversible processes near the crack tip at a relevant microscopic level. The first Subproblem, which prompts a phenomenological fracture theory, receives a thorough investigation in this paper. Griffith's energy accounting is extended to include energy change due to both deformation and polarization. Four modes of square root singularities are identified at the tip of a crack in a homogeneous piezoelectric. A new type of singularity is discovered around interface crack tips. Specifically, the singularities in general form two pairs: r1/2±ieand r1/2±ie, where e. and k are real numbers depending on the constitutive constants. Also solved is a class of boundary value problems involving many cracks on the interface between half-spaces. Fracture mechanics are established for ferroelectric ceramics under smallscale hysteresis conditions, which facilitates the experimental study of fracture resistance and fatigue crack growth under combined mechanical and electrical loading. Both poled and unpoled fcrroelectrie ceramics are discussed.

Family of crack-tip fields characterized by a triaxiality parameter—II. Fracture applications

Abstract: C entral to the J-based fracture mechanics approach is the concept of J-dominance whereby J alone sets the stress level as well as the size scale of the zone of high stresses and strains. In Part I the idea of a J Q annulus was developed. Within the annulus, the plane strain plastic near-tip fields are members of a family of solutions parameterized by Q when distances are normalized by J σ 0 , where σ0is the yield stress, J and Q have distinct roles: J sets the size scale over which large stresses and strains develop while Q scales the near-tip stress distribution and the stress triaxiality achieved ahead of the crack. Specifically, negative (positive) Q values mean that the hydrostatic stress is reduced (increased) by Qσ0 from the Q = 0 plane strain reference state. Therefore Q provides a quantitative measure of crack-tip constraint, a term widely used in the literature concerning geometry and size effects on a material's resistance to fracture. These developments are discussed further in this paper. It is shown that the J Q approach considerably extends the range of applicability of fracture mechanics for shallow-crack geometries loaded in tension and bending, and deep-crack geometries loaded in tension. The J Q theory provides a framework to organize toughness data as a function of constraint and to utilize such data in engineering applications. Two methods for estimating Q at fully yielded conditions and an interpolation scheme are discussed. The effects of crack size and specimen type on fracture toughness are addressed.

Linear electro-elastic fracture mechanics of piezoelectric materials

Abstract: The concepts of linear elastic fracture mechanics, generalized to treat piezoelectric effects, are employed to study the influence of the electrical fields on the fracture behavior of piezoelectric materials The method of distributed dislocations and electric dipoles, already existing in the literature, is used to calculate the electro-elastic fields and the energy-release rate for a finite crack embedded in an infinite piezoelectric medium which is subjected to both mechanical and electric loads The energy-release rate expressions show that the electric fields generally tend to slow the crack growth It is shown that the stress intensity factor criterion and the energy-release rate criterion differ when the energetics of the electric field is taken into account The study of crack tip singular stress field yields a possible explanation for experimentally observed crack skewing in the presence of a strong electric field

Strengthening of RC beams with epoxy-bonded fibre-composite materials

Abstract: Strengthening of concrete beams with externally bonded fibre-reinforced plastic (FRP) materials appears to be a feasible way of increasing the load-carrying capacity and stiffness characteristics of existing structures. FRP-strengthened concrete beams can fail in several ways when loaded in bending. The following collapse mechanisms are identified and analysed in this study: steel yield-FRP rupture, steel yield-concrete crushing, compressive failure, and debonding. Here we obtain equations describing each failure mechanism using the strain compatibility method, concepts of fracture mechanics and a simple model for the FRP peeling-off debonding mechanism due to the development of shear cracks. We then produce diagrams showing the beam designs for which each failure mechanism is dominant, examine the effect of FRP sheets on the ductility and stiffness of strengthened components, and give results of four-point bending tests confirming our analysis. The analytical results obtained can be used in establishing an FRP selection procedure for external strengthening of reinforced concrete members with lightweight and durable materials.

Fracture mechanics of concrete structures

Abstract: State-of-the-art report: Fracture mechanics of concrete: concepts, models and determination of material properties. Why fracture mechanics? Essential results from linear elastic fracture mechanics. Nonlinear fracture models with softening zone. Special nonlinear fracture models based on adaptions of LEFM. Size effect and brittleness of structures. Experimental or analytical determination of material fracture parameters. Factors influencing fracture parameters. Effect of reinforcement. Crack systems. Concluding remarks. References and bibliography. Appendix 1- derivations of some formulas. Conference papers. Material models for concrete fracture. Damage modelling. Numerical analysis of concrete fracture. Experimental methods and determination of fracture characteristics. Measurements of damage and size effect. Dynamic fracture. Fracture under shear. Fracture of reinforced concrete. Interaction between concrete and reinforcement. Fatigue and rate effects. Environment effects [temperature, shrinkage, corrosion]. Index.

Conditions for Pseudo Strain-Hardening in Fiber Reinforced Brittle Matrix Composites

Abstract: Apart from imparting increased fracture toughness, one of the useful purposes of reinforcing brittle matrices with fibers is to create enhanced composite strain capacity. This paper reviews the conditions underwhich such a composite will exhibit the pseudo strain-hardening phenomenon. The presentation is given in a unified manner for both continuous aligned and discontinuous random fiber composites. It is demonstrated that pseudo strain hardening can be practically designed for both gills of composites by proper tailoring of material structures. 18 refs., 8 figs., 2 tabs.

Rock fracture mechanics : principles, design, and applications

Abstract: Preface. Contents. List of Notations. 1. Introduction. 2. Some Fundamental Aspects of Mechanics. 3. The Griffith Theory and the Evolution of Modern Fracture Mechanics. 4. Linear Elastic Fracture Mechanics and Fracture Initiation Theories. 5. Determination of Stress Intensity Factors. 6. Aspects of Non-linear Elastic Fracture Mechanics. 7. Some Aspects of Statistical Fracture Mechanics. 8. Mode I Fracture Toughness Testing. 9. Mode II and Mixed Mode I-II Fracture Toughness Testing. 10. Interrelationships Between Fracture Toughness, Hardness Index and Physico-Mechanical Properties of Rocks. 11. Fracture Mechanics Applied to Hydraulic Fracture Propagation and In Situ Stress Determinations. 12. Fracture Mechanics Applied to Rock Fragmentation by Cutting Action. 13. Fracture Mechanics Applied to Rock Fragmentation due to Blasting. 14. Fracture Mechanics Applied to Analysis of Rockbursts. 15. Fracture Mechanics Applied to Design and Stability of Rock Slopes Engineering Problems. Appendix: A Compilation of Mode I Fracture Toughness Values of Rocks. References. Supplementary List of Recommended References. Index.

Asymmetric Shielding in Interfacial Fracture Under In-Plane Shear

Abstract: The toughness of a glass/'epoxy interface was measured over a wide range of mode mixes. A toughening effect was associated with increasing positive and negative in-plane shear components. Optical interference measurements of normal crack opening displacements near the crack front and complementary finite element analyses were used to examine near-front behavior during crack initiation. Estimates of the tough­ening based on plastic dissipation, bulk viscoelastic dissipation, and interface asperity shielding did not fully account for the measured values. The results suggest that the inelastic behavior of the epoxy, frictional, and, perhaps, three-dimensional effects should be considered. 1 Introduction Interfacial crack growth occurs in a number of applications of technological importance. Because of the fact that the frac­ture path is constrained irrespective of the orientation of the globally applied loads and also because of the mismatch of material properties across the interface, crack growth is in­herently mixed mode. Critical and subcritical crack growth must then be governed by some combination of mode I, II, and III fracture parameters. The simplest approach, using one parameter, seeks to determine an effective parameter that can account for all mode mixes in a unifying manner. This is particularly useful for subcritical crack growth where corre­lations of crack growth rates fall on one curve for all mode mixes when the proper parameter is found. An alternative is to consider a two-parameter approach where one parameter represents the mode mix or direction and the other a magni­tude. For critical crack growth, the magnitude will generally be a function of mode mix. The form the function is usually determined experimentally but may, as mechanisms are better understood, even be predicted. The most common approach for examining interfacial crack initiation has been to consider the interfacial fracture tough­ness, G

Tensile and tensile fatigue behaviour of concrete; experiments, modelling and analyses

Abstract: A model based on nonlinear fracture mechanics is presented for the fatigue behavior of plain concrete. The tensile behavior of concrete for a monotonic increasing deformation is described. The softening relation is described and the way the fracture mechanics parameters are influenced by several variables is shown. The behavior of a softening material subjected to a uniaxial tensile test is explained. Based on experimental results, a constitutive model for the crack cyclic behavior of concrete is proposed. The adequacy of the model is shown by numerical simulation of notched beams under 4-point bending. It is shown by experiments, that localization and non-uniform crack opening occurs in tensile fatigue tests just as in monotonic loaded tensile tests.

Dual boundary element method for three-dimensional fracture mechanics analysis

Abstract: In this paper, an effective numerical implementation of the three-dimensional dual boundary element method, for linear elastic crack problems, is presented. Displacement and traction integral equations which constitute the dual boundary formulation are used independently on crack surfaces to overcome the numerical difficulties associated with co-planar crack surfaces in boundary element analysis. The crack surfaces are modelled with discontinous quadrilateral quadratic elements. The use of discontinous elements allow for accurate integration of finite part integrals. The accuracy of the proposed method is demonstrated by solving a number of problems including edge and embedded cracks.

Instability in the propagation of fast cracks

Abstract: We report on experimental investigations of the propagation of cracks in the brittle plastic polymethyl methacrylate (PMMA). Velocity measurements with resolution an order of magnitude better than previous experiments reveal the existence of a critical velocity (330\ifmmode\pm\else\textpm\fi{}30 m/s) at which the velocity of the crack tip begins to oscillate, the dynamics of the crack abruptly change, and a periodic pattern is formed on the crack surface. Beyond the critical point the amplitude of the oscillations depends linearly on the mean velocity of the crack. The existence of this instability may explain the failure of theoretical predictions of crack dynamics and provides a mechanism for the enhanced dissipation observed experimentally in the fracture of brittle materials.

Postcrack Scaling Relations for Fiber Reinforced Cementitious Composites

Abstract: The prepeak and postpeak stress-displacement relations are derived for the bridging mechanism associated with randomly oriented discontinuous flexible fibers in cement-based composites. The postcrack strength and fracture energy are examined in light of the scaling micromechanical parameters, including fiber snubbing coefficient, diameter, aspect ratio, volume fraction, and interface bond strength. Comparisons of theoretically derived postcracking stress-displacement relation and pullout fracture energy with experimental data of both steel-fiber and synthetic-fiber reinforced cementitious composites of widely varying micromechanical parametric values suggest that the simple model approximates the bridging behavior in this type of composite.

The initiation and growth of delaminations induced by matrix microcracks in laminated composites

Abstract: A recent variational mechanics analysis of microcracking damage in cross-ply laminates of the form /(S)/90n/s, where (S) is any orthotropic sublaminate much stiffer than /90n/, has been extended to account for the presence of delaminations emanating from the tips of microcracks in the /90 2n/T sublaminate. The new two-dimensional stress analysis is used to calculate the total strain energy, effective modulus, and longitudinal thermal expansion coefficient for a laminate having microcracks and delaminations. These results are used to calculate the energy release rate for the initiation and growth of a delamination induced by a matrix microcrack. At low crack densities, /(S)/90n/s laminates are expected to fail by microcracking and to show little or no delamination. At some critical crack density, which is a function of laminate structure and material properties, the energy release rate for delamination exceeds that for microcracking and delamination is predicted to dominate over microcracking. A quasi-three-dimensional model is used to predict the propagation of arbitrarily shaped delamination fronts. All predictions agree with experimental observations.

Fracture energy and fracture process zone

Abstract: The fracture energy Gf can be determined following a RILEM recommendation. However, it has been found that fracture energy depends on both size and geometry of the test specimen. The underlying fictitious crack model postulates that fracture energy, tensile strength, the critical opening of the fictitious crack, and the shape of the softening curve (softening factor) are constants for a given type of concrete. Here it is shown that a local fracture energy ccan be introduced. This local fracture energy varies with the width of the fracture process zone. As the crack approaches the back end of a specimen the fracture process zone becomes more and more confined and hence the local fracture energy decreases. Theoretical predictions are compared with experimental results obtained with the wedge splitting technique described earlier. It is shown that a local variation of the fracture energy leads to a size dependence of the global specific fracture energy.

Measurement of the fracture energy using three-point bend tests: Part 1—Influence of experimental procedures

Abstract: Available measures of the fracture energy GF obtained with the procedure proposed by RILEM TC-50 provide values that appear to change with sample size, calling into question the possibility of considering GF as a material parameter. In this paper some possible sources of experimental errors, when the RILEM proposal is applied, are ascertained, namely the apparent energy dissipation from hysteresis in the testing equipment and energy dissipation in the lateral supports. It is concluded that either some other sources of energy dissipation are operative or that GF cannot be considered a material property.

Softening of concrete loaded in compression

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Measurement of the fracture energy using three-point bend tests: Part 2—Influence of bulk energy dissipation

Abstract: Avialable measures of the fracture energy GF obtained with the procedure proposed by RILEM TC-50 provide values that appear to change with sample size, calling into question whether GF can be considered as a material parameter. In a previous paper, possible sources of energy dissipation from the testing equipment and lateral supports were considered. In this paper new possible sources of energy dissipation in the sample, apart from the fracture crack itself, are considered. Such dissipation will take place inside the bulk of the most stressed regions of the specimen and, if it is not taken into account, higher values of GF will be recorded than that strictly due to surface fracture energy. When this constribution and the possible energy dissipation analysed in previous work are considered, they are not enough to account for the measured size effect. If GF is to be considered a material parameter, the evaluation of the results from the RILEM method should be analysed more carefully. In any case, the dissipated energy reported here represents a non-negligible amount of GF and should be taken into account when performing measurements.

Role of pore fluids in the generation of seismic precursors to shear fracture

Abstract: A SYSTEMATIC study of temporal changes in seismic b-values (defined as the log-linear slope of the earthquake frequency–magnitude distribution) has shown that large earthquakes are often preceded by an intermediate-term increase in b, followed by a decrease in the months to weeks before the earthquake1. The onset of the b-value increase can precede earthquake occurrence by as much as 7 years. A recently proposed fracture mechanics model of the earthquake source2 explains these temporal fluctuations in b in terms of the underlying physical processes of time-varying applied stress and crack growth. The model predicts two minima in b, separated by a short-lived maximum. Here we report the results of controlled laboratory deformation experiments, done in simulated upper-crustal conditions on both air-dried and water-saturated rock specimens. As found in previous experiments3–5, shear fracture in dry specimens is characterized by a decline in b during anelastic deformation to a single minimum reached just before failure. But in water-saturated specimens, when pore-fluid volume is kept constant by servo-control we also observe a second, intermediate-term b-value minimum, so reproducing the double b-value anomaly predicted by the model2.

On the analysis of mixed-mode failure

Abstract: The present paper is concerned with the problem of mixed-mode fracture, especially where such failure occurs along a plane of weakness at a bimaterial interface or by interlaminar failure in polymer fibre-composite materials Firstly, two different schemes for analysing such mixed-mode failures are discussed These schemes are: (i) a method based upon a consideration of the local singular field ahead of a crack tip, and (ii) a global method based upon a consideration of the applied energy release rates Secondly, experimental data taken from the literature are reviewed and it is concluded that the latter scheme results in a more consistent interpretation of the data Indeed, in several cases the global method clearly gives far better agreement between the theoretical predictions and the observed results The reasons for this are suggested to be the very localised nature of the singular-dominated region ahead of a crack tip in many test specimens and the relatively large damage zone in the materials studied Finally, the present work has led to the proposal of a general criterion for fracture under mixed-mode loading

Influence of microstructure on crack-tip micromechanics and fracture behaviors of a two-phase TiAl alloy

Abstract: The tensile deformation, crack-tip micromechanics, and fracture behaviors of a two-phase (γ + α2) gamma titanium aluminide alloy, Ti-47Al-2.6Nb-2(Cr+V), heat-treated for the microstructure of either fine duplex (gamma + lamellar) or predominantly lamellar microstructure were studied in the 25 °C to 800 °C range.In situ tensile and fracture toughness tests were performed in vacuum using a high-temperature loading stage in a scanning electron microscope (SEM), while conventional tensile tests were performed in air. The results revealed strong influences of microstructure on the crack-tip deformation, quasi-static crack growth, and the fracture initiation behaviors in the alloy. Intergranular fracture and cleavage were the dominant fracture mechanisms in the duplex microstructure material, whose fracture remained brittle at temperatures up to 600 °C. In contrast, the nearly fully lamellar microstructure resulted in a relatively high crack growth resistance in the 25 °C to 800 °C range, with interface delamination, translamellar fracture, and decohesion of colony boundaries being the main fracture processes. The higher fracture resistance exhibited by the lamellar microstructure can be attributed, at least partly, to toughening by shear ligaments formed as the result of mismatched crack planes in the process zone.