Showing papers on "Fracture mechanics published in 1983"
01 May 1983
TL;DR: In this article, a fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed.
Abstract: A fracture theory for a heterogenous aggregate material which exhibits a gradual strain-softening due to microcracking and contains aggregate pieces that are not necessarily small compared to structural dimensions is developed. Only Mode I is considered. The fracture is modeled as a blunt smeard crack band, which is justified by the random nature of the microstructure. Simple triaxial stress-strain relations which model the strain-softening and describe the effect of gradual microcracking in the crack band are derived. It is shown that it is easier to use compliance rather than stiffness matrices and that it suffices to adjust a single diagonal term of the complicance matrix. The limiting case of this matrix for complete (continuous) cracking is shown to be identical to the inverse of the well-known stiffness matrix for a perfectly cracked material. The material fracture properties are characterized by only three parameters—fracture energy, uniaxial strength limit and width of the crack band (fracture process zone), while the strain-softening modulus is a function of these parameters. A method of determining the fracture energy from measured complete stres-strain relations is also given. Triaxial stress effects on fracture can be taken into account. The theory is verified by comparisons with numerous experimental data from the literature. Satisfactory fits of maximum load data as well as resistance curves are achieved and values of the three material parameters involved, namely the fracture energy, the strength, and the width of crack band front, are determined from test data. The optimum value of the latter width is found to be about 3 aggregate sizes, which is also justified as the minimum acceptable for a homogeneous continuum modeling. The method of implementing the theory in a finite element code is also indicated, and rules for achieving objectivity of results with regard to the analyst's choice of element size are given. Finally, a simple formula is derived to predict from the tensile strength and aggregate size the fracture energy, as well as the strain-softening modulus. A statistical analysis of the errors reveals a drastic improvement compared to the linear fracture theory as well as the strength theory. The applicability of fracture mechanics to concrete is thus solidly established.
3,102 citations
TL;DR: In this paper, the authors review the analysis of composite materials from the applied mechanics and engineering science point of view, including elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity, static strength, and fatigue failure.
Abstract: The purpose of the present survey is to review the analysis of composite materials from the applied mechanics and engineering science point of view. The subjects under consideration will be analysis of the following properties of various kinds of composite materials: elasticity, thermal expansion, moisture swelling, viscoelasticity, conductivity (which includes, by mathematical analogy, dielectrics, magnetics, and diffusion) static strength, and fatigue failure.
2,216 citations
TL;DR: In this article, a fracture mechanics approach has been used to predict fracture toughness increases due to crack deflection around second phase particles, based on a determination of the initial tilt and the maximum twist of the crack front between particles.
1,287 citations
TL;DR: In this article, a local criterion based on Weibull theory was proposed to determine the mechanical conditions for cleavage fracture at the crack tip of A508 class 3 steel, and the results can be accounted for in terms of the local criterion which takes into account the effect of plastic strain.
Abstract: Experiments were performed on three heats of A508 class 3 steel in order to determine the mechanical conditions for cleavage fracture. These tests were carried out on various geometries including 4-point bend specimens and axisymmetric notched tensile bars with different notch radii which have been modelized using the finite element method. In one heat, the temperature range investigated was from 77 K to 233 K. It is shown that the cleavage resistance is increased by tensile straining. Moreover, the probability of fracture obeys the Weibull statistical distribution. All the results can be accounted for in terms of a local criterion based on Weibull theory and which takes into account the effect of plastic strain. In this criterion, the parameters which were experimentally determined are found to be temperature independent over the range 77 K to 170 K. The applicability of the approach proposed for cleavage fracture at the crack tip is also examined. It is shown that the experimental results published in the literature giving the variation of fracture toughness with temperature can be explained by the proposed criterion which predicts reasonably well both the scatter in the experimental results and theKICtemperature dependence.
1,090 citations
TL;DR: In this article, the authors considered the plane elasticity problem for a nonhomogeneous medium containing a crack and derived the integral equation having the derivative of the crack surface displacement as the density function.
Abstract: The plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square root singularity. The solution is given for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible.
711 citations
TL;DR: In this article, the microstructure and fracture behavior of an unmodified and a rubber-modified epoxy have been studied and the mechanisms for this increased toughness have been considered and a mechanism that accounts for all the observed characteristics has been proposed.
708 citations
690 citations
354 citations
TL;DR: In this article, the fundamental mechanical aspects of dynamic fracture in metals are presented, with emphasis on spalling produced by the interactions of shock and reflected tensile waves, and the major research efforts conducted in this area are reviewed; the process has been successfully described as a sequence of nucleation, growth, and coalescence of voids or cracks.
315 citations
TL;DR: In this article, a qualitative mechanism involving cavitation, shear yielding and plastic flow was proposed to calculate values of the crack opening displacement and the correlations established between stress intensity factor, KIc, yield stress and type of crack growth suggest that the extent of crack tip blunting largely governs the relative toughness of the epoxy materials.
310 citations
TL;DR: In this paper, the concept of the stress intensity factor, the underlying mechanics problem leading to its emergence, and its physical relevance, particularly its relation to fracture mechanics are discussed, and the reasons as to why it has become nearly an indispensable tool for studying such important phenomena as brittle fracture and fatigue or corrosion fatigue crack propagation in structural solids are considered.
Abstract: In this work the concept of the stress intensity factor, the underlying mechanics problem leading to its emergence, and its physical relevance, particularly its relation to fracture mechanics are discussed. The reasons as to why it has become nearly an indispensable tool for studying such important phenomena as brittle fracture and fatigue or corrosion fatigue crack propagation in structural solids are considered. A brief discussion of some of the important methods of solution of elastic crack problems is given. Also, a number of related special mechanics problems are described. 24 references.
TL;DR: In this paper, the failure modes of local buckling in beam flanges and fracture at weldments were studied in detail, and cumulative damage models were proposed which permit a life prediction for arbitrary cyclic loading histories.
TL;DR: In this article, the physical meaning of pathindependent integrals for elastodynamically propagating cracks introduced earlier by Atluri, Bui and Kishimoto et al. is addressed.
24 Sep 1983-Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences
TL;DR: In this paper, a theory is formulated to connect the strength of cement paste with its porosity, which shows that bending strength is largely dictated by the length of the largest pores, but there is also an influence of the volume of porosity which affects toughness through changing elastic modulus and fracture energy.
Abstract: A theory is formulated to connect the strength of cement paste with its porosity. The theory shows that bending strength is largely dictated by the length of the largest pores, as in the Griffith (1920) model, but there is also an influence of the volume of porosity, which affects toughness through changing elastic modulus and fracture energy. Verification of this theory was achieved by observing the large pores in cement, and then relating bending strength to the measured defect length, modulus and fracture energy. The argument was proved by developing processes to remove the large pores from cement pastes, thereby raising the bending strength to 70 MPa. Further removal of colloidal pores gave a bending strength of 150 MPa and compression strength up to 300 MPa with improved toughness. Re-introduction of controlled pores into these macro-defect-free (mdf) cements allowed Feret’s law (1897) to be explained.
TL;DR: In this paper, the authors investigated the influence of notch depth, specimen geometry, mean grain size and deformation velocity on the crackresistance force (R) in polycrystalline alumina.
Abstract: Fracture experiments under conditions of slow crack growth were performed with prenotched three-point bend specimens of polycrystalline alumina. The influence of notch depth, specimen geometry, mean grain size and deformation velocity on the crackresistance force (R) was investigated. Within one specimen R increases with crack propagation up to a factor of 4 (R-curve) accompanied by small changes (slight decrease) in crack velocity. No unique R-curve exists for these ceramics. Both the shape and the position of the R-curve are influenced by deformation velocity and notch depth. The latter effect means that for a certain crack length, R is larger in a specimen with the shorter notch (memory effect). The results are discussed in terms of energy dissipation by microcracks. The significance of both single R value and R-curve for fracture characterization of polycrystalline alumina is questioned.
[...]
TL;DR: In this article, it is proposed that the atomically sharp crack should be taken as the cornerstone for modeling propagation processes at the fundamental level, and electron microscopy evidence is presented in support of this contention.
Abstract: The underlying physical bases of present-day fracture theory are examined. It is proposed that the atomically sharp crack should be taken as the cornerstone for modeling propagation processes at the fundamental level. lkansmission electron microscopy evidence is presented in support of this contention. Linear continuum fracture mechanics is shown to have intrinsic limitations in its capacity to describe crack-tip phenomena; a more realistic description is provided by lattice statics, incorporating the picture of a crack as a narrow slit terminated by nonlinear linkage bonds. This description establishes a powerful starting point for understanding and predicting the effects of important crack-tip interaction processes.‘pwo such processes, chemically enhanced slow crack growth and process-zone toughening, are discussed in this light. Finally, the nature of strength-controlling flaws in brittle ceramics is considered, with particular reference to the validity of the widely adopted hypothesis that such flaws may be regarded as true micro-cracks.
TL;DR: In this article, a fracture mechanics approach to the well-known delamination problem in composite materials is presented, based on the theory of anisotropic laminate elasticity and interlaminar fracture mechanics concepts.
Abstract: A fracture mechanics approach to the well-known delamination problem in composite materials is presented. Based on the theory of anisotropic laminate elasticity and interlaminar fracture mechanics concepts, the composite delamination problem is formulated and solved. The exact order of the delamination crack-tip stress singularity is determined. Asymptotic stress and displacement fields for an interlaminar crack are obtained. Fracture mechanics parameters such as mixed-mode stress intensity factors, KI, KII, KIII, and the energy release rate, G, for composite delamination problems are defined. To illustrate the fundamental nature of the delamination crack behavior, solutions for edge-delaminated graphite-epoxy composites under uniform axial extension are presented. Effects of fiber orientation, ply thickness, and delamination length on the interlaminar fracture are examined.
01 Jan 1983
TL;DR: In concrete most cracks start from an uncracked surface and grow through a large portion of the depth of the specimen as mentioned in this paper, and both formation and growth are influenced by stresses from imposed deformations, shrinkage, temperature etc.
Abstract: In concrete most cracks start from an uncracked surface and grow through a large portion of the depth of the specimen. Both formation and growth are influenced by stresses from imposed deformations, shrinkage, temperature etc. Thus fracture mechanics, when applied to concrete, should be able to analyse the following: 1. The formation of a crack in a specimen which is not notched or precracked. 2. The growth of a crack to a size of the same order as that of the specimen. 3. The influence of imposed deformations on crack formation and crack growth.(30 refs)
TL;DR: In this article, a modified indentation technique for measuring toughness is described, which retains the elastic/plastic basis of previous contact fracture descriptions but eliminates explicit reference to residual stress parameters in the toughness formulation.
Abstract: A modified indentation technique for measuring toughness is described. The method retains the elastic/plastic basis of previous contact fracture descriptions but eliminates explicit reference to residual stress parameters in the toughness formulation. Accordingly, improved correlations between indentation data and “conventional” Kc values are obtained, even for materials (e.g. anomalous glasses) with nonideal deformation responses.
TL;DR: In this article, a model derived from the mechanics of tensile microcracks is presented which describes the deformation of brittle rock, and the model employs the assumption that stress and time-dependent microcrack growth is responsible for the inelastic deformation.
Abstract: A continuum model derived from the mechanics of tensile microcracks is presented which describes the deformation of brittle rock. The model employs the assumption that stress and time-dependent microcrack growth is responsible for the inelastic deformation. Microcrack growth is assumed to occur by two mechanisms: stress-induced crack growth (time independent) and stress corrosion (stress and time dependent). From the analysis of individual cracks a criterion for the initiation of damage (crack growth) is derived. This results in the specification of initial and subsequent damage surfaces in stress space which are similar to yield surfaces in the theory of plasticity. When the stress state is below the damage surface, no stress-induced crack growth can take place. For stress states on the damage surface, crack growth accompanies any increase in loading, thus expanding the damage surface. By generalizing the results obtained from the analysis of single cracks, a continuum description of the behavior of an ensemble of cracks in an otherwise elastic body is derived. The resulting constitutive equation is essentially elastic but accounts for material behavior due to microcrack growth through the inclusion of an internal state variable which is a measure of the crack state. The form of the evolutionary equation for the crack state parameter is determined from the fracture mechanics analysis of single cracks and experimental results on time-dependent crack growth in rock. Model simulations of quasi-static uniaxial and triaxial compression tests are presented, and the results are compared to the results of a similar laboratory test on Westerly granite.
TL;DR: In this paper, a model of cavity nucleation based on the stochastic nature of transgranular creep deformation is presented, and a quantitative assessment of the likely errors of measurement is presented.
TL;DR: In this paper, the effect of grain boundary structure on creep intergranular fracture on metal bicrystals and polycrystals is discussed on the basis of the effect on sliding, the contribution of sliding to the overall creep deformation and a sliding-fracture diagram.
Abstract: Importance of grain boundary sliding to creep intergranular fracture is focussed. Previous metallographic and fractographic studies of creep intergranular fracture on metal bicrystals and polycrystals are briefly reviewed in order to show the close relationship between grain boundary sliding and fracture. Deformation ledge and migration irregularity are shown to be potential sites of stress concentration and crack nucleation on sliding grain boundaries without particles. The effect of grain boundary structure on creep intergranular fracture is discussed on the basis of the effect of grain boundary structure on sliding, the contribution of sliding to the overall creep deformation, and a sliding-fracture diagram. Recent observations of the effect of grain boundary structure on creep intergranular fracture on alpha iron-tin alloy polycrystals are shown.
TL;DR: A review of the literature on the ductile fracture of metals and alloys reveals almost immediately that the majority of investigations approach the topic from a fracture mechanics point of view and that papers based entirely on microstructural research are rare as discussed by the authors.
TL;DR: In this article, the fracture initiation characteristics under general combination of the opening mode, sliding mode and tearing mode were investigated both theoretically and experimentally. And the experimental fracture strengths were compared with those predicted by the fracture criteria which are represented in terms of: (1) maximum tangential stress, [σgq]max, extended to general combined modes, (2) maximum energy release rate at the propagation of a small kinked crack, [Gk(γ)]max, and (3) newly derived maximum EE at the initiation of an EH burst, [
TL;DR: In this article, the authors measured the distribution of crack spacings developed in the 90° ply of 0°/90°/0° glass fiber/epoxy resin laminates under tensile loading and showed that the ply has a variable strength.
Abstract: Measurements of the distributions of crack spacings developed in the 90° ply of 0°/90°/0° glass fibre/epoxy resin laminates under tensile loading show that the ply has a variable strength. As a consequence the strain at which cracking begins is very dependent on the specimen length. The observed distributions of crack spacing are not consistent with the assumption of a uniform strength for the 90° ply. A statistical model provides a good description of the cracking behaviour particularly when the cracks are widely spaced. Magnification of the stress in the matrix between the relatively stiff glass fibres leads to debonding which is observed as a reversible “stress-whitening.” The distributions reveal a lower probability of crack formation in the under-stressed region close to the existing cracks and provide estimates of the size of this region. The method of analysis can be applied to many systems which exhibit multiple fracture.
TL;DR: In this article, a new statistical theory is proposed for the analysis of fatigue crack propagation, based on the concepts of fracture mechanics and random processes, and a recursive relationship is obtained for the statistical moments of this random time for a rather general class of material behaviors, and examples are given for the case where the crack propagation rate is governed by a power law.
TL;DR: In this article, the authors examined hydrogen embrittlement in FeSi-and Ni-single crystals at low hydrogen pressures (10 mPa ⩽ pH2⩽ 100 kPa) and measured the crack tip opening angle α of a growing crack as a function of temperature, hydrogen pressure and rate.