Showing papers on "Fracture mechanics published in 1981"

A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness: I, Direct Crack Measurements

Abstract: The application of indentation techniques to the evaluation of fracture toughness is examined critically, in two parts. In this first part, attention is focused on an approach which involves direct measurement of Vickers-produced radial cracks as a function of indentation load. A theoretical basis for the method is first established, in terms of elastic/plastic indentation fracture mechanics. It is thereby asserted that the key to the radial crack response lies in the residual component of the contact field. This residual term has important implications concerning the crack evolution, including the possibility of post indentation slow growth under environment-sensitive conditions. Fractographic observations of cracks in selected “reference” materials are used to determine the magnitude of this effect and to investigate other potential complications associated with departures from ideal indentation fracture behavior. The data from these observations provide a convenient calibration of the Indentation toughness equations for general application to other well-behaved ceramics. The technique is uniquely simple in procedure and economic in its use of material.

Crack growth and development of fracture zones in plain concrete and similar materials

Abstract: A calculation model (the Fictitious Crack Model), based on fracture mechanics and the finite element method, 1s presented. In the model the fracture zone in front of a crack is represented by a fictitious crack that 1s able to transfer stress. The stress transferring capability of the fictitious crack normally decreases when the crack width increases. The applicability of linear elastic fracture mechanics to concrete and similar materials is analysed by use of the Fictitious Crack Model. It" Is found that linear elastic fracture mechanics 1s too dependent on, among other things, specimen dimensions to be useful as a fracture approach, unless the dimensions, for concrete structures, are in order of meters. The usefulness of the J-integral, the COD-approach and the R-curve analysis is also found to be very limited where cementitious materials are concerned. The complete tensile stress-strain curve is introduced as a fracture mechanical parameter. The curve can be approximatively determined if the tensile strength, the Young's modius and the fracture energy are known. Su1table~lest methods Tor determining" TRise~~/'Voerties are presented and test results are reported for a number of concrete qua! » a. A new tyr * very stiff tensile testing machine Is presented by which it is possible to carry r . itable tensile tests on concrete. The complete tensile stress-strain curves h •«• feen determined for a number of concrete qualities. The thesi' overs a complete system for analysing crack propagation in concrete as it Include* -ealistic material model, a functional calculation model and methods for determiv" «/ the material properties necessary for the calculations. Therefore this work oi r t to be of use as a base for further studies of the fracture process of concrete < i similar materials.

A crack-closure model for predicting fatigue crack growth under aircraft spectrum loading

Abstract: The development and application of an analytical model of cycle crack growth is presented that includes the effects of crack closure. The model was used to correlate crack growth rates under constant amplitude loading and to predict crack growth under aircraft spectrum loading on 2219-T851 aluminum alloy sheet material. The predicted crack growth lives agreed well with experimental data. The ratio of predicted to experimental lives ranged from 0.66 to 1.48. These predictions were made using data from an ASTM E24.06.01 Round Robin.

Two‐dimensional stress intensity factor computations using the boundary element method

Abstract: A multidomain boundary element formulation for the analysis of general two-dimensional plane strain/stress crack problems is presented. The numerical results were accurate and efficient. The analyses were performed using traction singular quater-point boundary elements on each side of the crack tip(s) with and without transition elements. Traction singular quarter-point boundary elements contain the correct √r displacement and 1/√r traction variations at the crack tip. Transition elements are appended to the traction singular elements to model the √r displacement variation. The 1/√r traction singularity is not represented with these elements. Current research studies for the crack propagation analysis of quasi-static and fatigue fracture problems are discussed.

Fracture mechanics studies of crack healing and welding of polymers

Abstract: Compact tension tests have been performed on re-healed and welded glassy polymers (PMMA-PMMA, SAN-SAN and PMMA-SAN). At temperatures above the glass transition temperature,Tg, it was observed that the facture toughness,KIi, in the interface increased with contact time,t, asKIi ∝t1/4 as predicted by a diffusion model. The self-diffusion constantD(Tg + 15 K) of chains of molecular weight 1.2×105 can be estimated as 1×10−21sec−1 with an activation energy of 274 kJ mol−1. For full material resistance, the depth of interdiffusion, 〈Δx2〉1/2, was calculated to be between 2 and 3 nm. Vacuum drying of the specimens, as well as polishing the interfaces, decreases the speed of interdiffusion.

Stress-intensity factor equations for cracks in three-dimensional finite bodies

Abstract: Empirical stress intensity factor equations are presented for embedded elliptical cracks, semi-elliptical surface cracks, quarter-elliptical corner cracks, semi-elliptical surface cracks at a hole, and quarter-elliptical corner cracks at a hole in finite plates. The plates were subjected to remote tensile loading. Equations give stress intensity factors as a function of parametric angle, crack depth, crack length, plate thickness, and where applicable, hole radius. The stress intensity factors used to develop the equations were obtained from three dimensional finite element analyses of these crack configurations.

Preparation, microstructure and mechanical properties of dense polycrystalline hydroxy apatite

Abstract: Hydroxy apatite ceramic blocks of varying density have been prepared from a commercial powder. The elastic properties, fracture toughness, strength and sub-critical crack growth of these materials have been investigated. Young's modulus for the nearly fully dense material is 112 GPa while the compressive strength is about 800 MPa. For the same material the strength and fracture toughness under dry conditions are 115 MPa and 1.0 MPa m1/2, respectively. Substantial slow crack growth was found under these conditions. Under wet conditions the values for strength and fracture toughness drop to about 75% of their “dry” values. In this case very serious slow crack growth is present.

The Fracture Resistance of a Toughened Epoxy Adhesive

Abstract: The fracture resistance of a rubber-modified epoxy adhesive has been studied using a continuum fracture-mechanics analysis. The fracture energy, G Ic , has been ascertained over a range of test temperatures and rates, both in bulk and in adhesive joints, as a function of specimen geometry. The results obtained are described and a semi-quantitative model discussed for predicting the joint failure behaviour from the bulk adhesive properties.

Elastic stress intensity factors evaluated by caustics

Abstract: The practical usefulness of the concept of the stress intensity factor at a crack tip in an elastic medium in the theory of fracture mechanics has led to a variety of theoretical, as well as experimental techniques for the evaluation of these factors Most of them concern the case of a crack inside an isotropic elastic medium under generalized plane stress or plane strain conditions, but several other cases have also extensively considered in the literature Among the first theoretical treatments of crack problems in plane isotropic elasticity we can mention those included in the well-known monograph by Muskhelishvili [1], as well as in the well-known paper by Westergaard [2] Today thousands of papers reporting elasticity solutions of crack problems and providing formulas and diagrams for the evaluation of stress intensity factors at crack tips can be found in the literature and are referenced in the recently appeared handbooks for the evaluation of stress intensity factors by Tada, Paris and Irwin [3] and Rooke and Cartwright [4] Furthermore, the most important theoretical techniques for the solution of plane elasticity crack problems and the evaluation of stress intensity factors were reviewed by Paris and Sih [5] and Sih [6] in the first volume of this series

Methods and models for predicting fatigue crack growth under random loading

Abstract: Papers are presented in the volume summarizing the baseline data, methodology, procedures, and results of a round-robin analysis which was conducted to predict the fatigue crack growth in 2219-T851 aluminum center-cracked specimens subjected to flight loading in random cycle-by-cycle format. The objective of the analysis was to assess whether data from constant-amplitude fatigue crack growth tests on center-cracked specimens can be used to predict fatigue crack growth lives under random loading. The following approaches are discussed in detail: a root-mean-square approach, a crack-closure model, a multi-parameter yield zone model, and a load-interaction model.

Recent progress in understanding environment assisted fatigue crack growth

Abstract: Metal fatigue has been well recognized as an important cause for failure of engineering structures. In most applications, fatigue damage results from the conjoint actions of the cyclically applied stress and the external (chemical) environment, and is therefore time dependent. Understanding of this load-environment interaction is essential to the formulation of rational life prediction procedures and to the development of realistic materials evaluation and qualification tests. Research over the past 15 years has led to the suggestion that the rate of fatigue crack growth in an aggressive environment, (da/dN)e, is the sum of three components—the rate of fatigue crack growth in an inert environment, (da/dN)r, which represents the contribution of “pure” fatigue, a cycle-dependent component, (da/dN)cf, that requires the synergistic interaction of fatigue and environmental attack, and the contribution by sustained-load crack growth (i.e., stress corrosion cracking) at K levels above K Iscc, (da/dN)scc. Recent fracture mechanics and surface chemistry studies have provided a clearer understanding of the cycle-dependent term, and, hence, a more complete understanding of environment assisted fatigue crack growth. (da/dN)cf results from the reaction of the environment with fresh crack surfaces produced by fatigue, and is a function of the extent of reaction during one loading cycle. For highly reactive alloy-environment systems, this contribution depends also on the rate of transport of the aggressive environment to the crack tip. The experimental basis and the development of models for transport and surface reaction controlled fatigue crack growth are reviewed. Interpretation of the effects of partial pressure of the aggressive environment and cyclic load frequency in terms of surface reaction and transport processes is discussed. Implications in terms of service performance and life prediction procedures are considered.

Grain‐Size Dependence of Fracture Energy in Ceramics: II, A Model for Noncubic Materials

Abstract: A mathematical model of the grain-size dependence of fracture energy of noncubic ceramics is developed and discussed. This model attributes the maxima in fracture energy of noncubic materials to countertrends of increasing numbers of microcracks and decreasing energy absorption per microcrack as grain size increases. The model predicts results similar to those experimentally observed. Agreement between calculated and measured fracture energy values is generally good, except for materials with extreme anisotropy. Sources of these differences and methods of improving calculations are discussed.

The fracture of an epoxy polymer containing elastomeric modifiers

Abstract: The fracture energies of elastomer-modified epoxy polymers have been determined over a range of strain rates from 10−2 to 103 sec−1. The modifiers included a liquid carboxyterminated butadiene acrylonitrile and a solid rubber. They were used alone and also in combination. In all cases, the modifiers increased the toughness of the base resin by orders of magnitude and one combination of liquid and solid rubber increased toughness by 60 times. There was a general decrease in fracture energy with increasing strain rate but even during impact testing the modified epoxys were 10 to 20 times tougher than the base polymer. Scanning electron microscopy revealed that, when combined with the liquid rubber, the solid rubber induced a localized shear yielding.

Simulation of crack propagation and failure of concrete

Abstract: First of all the heterogeneous structure of concrete is described in terms of a multi-level system. To take different effects of crack propagation and crack arresting into consideration, four different levels have been introduced. Conditions for crack propagation in the porous structure of hardened cement paste and in a matrix with inclusions are studied analytically. By using the derived formulae crack formation and failure of lightweight, normal, and high strength concrete are discussed. Computer experiments are described. It is shown that crack propagation and final degradation of composite structures can be simulated realistically. Finally some supplementing experiments are mentioned. Experimental results are in reasonable agreement with theoretical predictions.

Static and energetic fracture parameters for rocks and concretes

Abstract: The object of the paper is to determine the fracture toughness parameters K1C,G1C and J1C for some aggregative materials. Values of the J-integral are calculated from load-displacement curves, following the procedure suggested by Begley and Landes for steel alloys. Some recurring experimental incoherences are explained applying Buckingham's Theorem for physical similitude and scale modeling to Fracture Mechanics. Thus a non-dimensional parameter can be defined (the test brittleness number), which governs the fracture-sensitivity phenomenon. The fracture parameters K1C and J1C are connected by a fictitious Young's modulus E*, which is lower than the real modulus E and represents the stiffness of the damaged material near the crack tip before the extension. When the specimen sizes are so small that the material becomes fracture insensitive, then E* appears higher than E.

Tackiness of Elastomers

Abstract: Probe tack testing procedure can be analysed by the fracture mechanics theory previously proposed by the authors for adherence of spheres or punches at fixed load or fixed grips conditions. Tack curves obtained by computer integration closely coincide with experimental ones. So, the influence of various parameters such as cross-head velocity, stiffness of the testing machine or temperature, on tackiness can be predicted.

Small Crack Behavior and the Prediction of Fatigue Life

Abstract: It is becoming increasingly evident that an understanding of incipient microcracking and growth of small cracks is essential to the development of improved predictions of the fatigue life of structures. Information on the threshold and kinetic properties of small cracks is reviewed and critically discussed. It is shown that the use of conventional fracture mechanics concepts to characterize small cracks results in behavior which differs from that of large cracks—this difference is due to a breakdown of underlying continuum mechanics assumptions. Methods to incorporate small crack behavior in fatigue life predictions are also considered. In these predictions, the importance of separately treating crack initiation and crack growth and of accounting for small crack behavior and plasticity effects (particularly for notched members) is demonstrated.

Fatigue analysis of brittle materials using indentation flaws

Abstract: A two-part study has been made of the fatigue characteristics of brittle solids using controlled indentation flaws In this part a general theory is developed, with explicit consideration being given to the role played by residual contact stresses in the fracture mechanics to failure The distinctive feature of the formulation is a stress intensity factor for well-defined indentation cracks, suitably modified to incorporate the residual component Taken in conjunction with a standard power-law crack velocity function, this leads to a differential equation for the dynamic fatigue response of a given material/ environment system Reduced variables are then introduced to facilitate generation of “universal” fatigue curves, determined uniquely by the crack velocity exponent,n A scheme for using these curves to evaluate basic fracture parameters from strength data is outlined In this way the foundation is laid for lifetime predictions of prospective brittle components, as well as for reconstruction of the crack velocity function One of the major advantages of the analysis is the manner in which the residual stress parameters are accommodated in the normalized fracture mechanics equations: whereas it is understood thatall strength data are to be taken from test pieces in their as-indented state, so making it unnecessary to have to resort to inconvenient stress-removal procedures between the contact and failure stages of testing,a priori knowledge of the residual stress level is not required The method is proposed as an economical route to materials evaluation and offers physical insight into the behaviour of natural flaws

Three‐dimensional spontaneous rupture propagation and implications for the earthquake source mechanism

Abstract: Summary We consider spontaneous cracks spreading out areally over a fault plane in an infinite medium as a realistic earthquake source model. The boundary integral equation technique described in Das is used to determine the displacements and stresses everywhere on the crack plane. For faults spreading out symmetrically in all four quadrants over infinite planes of constant yield strength, we find that the terminal rupture velocity VIIICR in the direction of purely anti-plane rupture is given by VIIICR < β. In the purely in-plane direction of rupture propagation, we find the terminal rupture velocity VIICR to be given by VIICR < α or VIICR < 0.5α, depending on the yield strength. We also find that crack propagation in the purely antiplane direction does not influence crack propagation in the purely in-plane direction and vice versa. For infinitely long shear cracks of finite width, the slip at a point is found to grow more slowly after the arrival of a shear wave diffracted from the nearer crack edge. The slip virtually ceases after the shear arrival from the further crack edge. This implies that for such faults the slip is controlled by the fault width. For a rectangular fault in an infinite medium, our final dynamic solution is in closer agreement with the static elliptical crack solution of Eshelby than with the static rectangular ‘dislocation model’ solution of Chinnery. We find the relationship between the average slip ū and average dynamic stress drop τe on such a rectangular fault of half-width W to be τe= Cμ(ū/W), where c ˜ 0.7. The slip at an interior point is again controlled by the fault width for faults that are much longer than wide so that the slip may stop in the region where the fault initiated before the completion of the rupture process. This implies that two rectangular faults of varying lengths but of the same width have the same slip for the same average stress drop, a fact clearly contradicted by observations that fault slip increases with earthquake size for great earthquakes occurring along the same fault. This contradiction is resolved if stress drops are also bigger for bigger earthquakes.

Resonance phenomena of Lamb waves scattering by a finite crack in a solid layer

Abstract: The paper is concerned with diffraction of Lamb waves by a finite crack, parallel to surfaces, in an elastic layer. The solution is constructed by the method of multiple diffractions at the edges of the crack. It is shown that the solution is identical with the solution obtained previously by the generalized Wiener–Hopf method. The resonance phenomena associated with the diffraction of Lamb waves by a finite crack are analyzed. The contribution of the different Lamb waves, generated in the crack zone, to the transmitted and reflected fields, is considered. An approximation of the solution, associated with incorporation of a finite number of Lamb waves, excited in the region of the layer occupied by the crack is discussed. Simple approximate equations are presented for resonance frequencies.