Showing papers on "Strain energy release rate published in 1982"

On the energy release rate and the J -integral for 3-D crack configurations

Abstract: In this paper an analytical expression for the energy release rate has been derived and put in a form suitable for a numerical analysis of an arbitrary 3-D crack configuration. The virtual crack extension method can most conveniently be used for such a derivation. This method was originally developed from finite element considerations and the resulting expressions were, therefore, based on the finite element matrix formulation [1–5]. In this paper the derivation of the energy release rate leads to an expression which is independent of any specific numerical procedure. The formulation is valid for general fracture behavior including nonplanar fracture and shear lips and applies to elastic materials as well as materials following the deformation theory of plasticity. The body force effect is also included. For 3-D fracture problems it is of advantage to use both an average and a local form of the energy release rate and definitions for both forms are suggested. For certain restrictions on the crack geometry it is shown that the energy release rate reduces to the 3-D form of the J-integral.

A Double Cantilever Beam Test for Characterizing Mode I Delamination of Composite Materials

Abstract: The double cantilever beam test is examined as a candidate for measuring in terlaminar fracture resistance as related to normal stress induced delamina tion. A number of approaches to data reduction schemes used in conjunction with this test method for determining critical strain energy release rate are discussed. Experimental data on unidirectional tape and bidirectional cloth graphite fiber reinforced polymeric matrix composites are compared to assess the potential of the double cantilever beam test as a materials screening tool. Matrix materials of varying inherent toughness were chosen for comparative purposes. Center notch data for 90-degree unidirectional graphite-epoxy composites were also obtained as a basis for test method comparison.

Interlaminar Fracture of Composite Materials

Abstract: Interlaminar fracture characteristics of a graphite/epoxy composite material (AS1/3501-6) are investigated under the opening, shearing and mix ed mode conditions. The Arcan test fixture was modified to accomodate the composite specimen containing an embedded interlaminar crack. Both critical stress intensity factor and strain energy release rate data were deter mined and the quadratic interaction for mixed mode behavior was compared to experimental data. Results of over sixty tests showed that the test fixture yielded results which compare favorably with results from contemporary test fixtures. Critical fracture parameters for the opening and shearing modes were shown to differ by a factor of 9.1. Further, the test results showed general agreement with the quadratic interaction relation.

Slow Crack Growth in Cement Composites

Abstract: The resistance to crack growth in mortar, concrete and fiber reinforced concrete was studied by testing double torsion and double cantilever speciments. R-curves (plots of strain energy release rate vs. crack extension) were obtained from the test data. To include the inelastic strain energy absorbed during the crack extension, the definition of the strain energy release rate was modified. It was found that R-curves for mortar and concrete were similar for both double torsion and double cantilever speciments. R-curves were sensitive to the volume and size of aggregates and to the presence of fibers. It appears that R-curves can be a useful specimen-geometry-independent parameter for chracterizing the fracture behavior of cementitious composites. However, the effects of differing crack-opening displacement on the strain energy release rate must be considered; especially for fiber reinforced concrete.

The interface crack with a contact zone (an analytical treatment)

Abstract: An analytical treatment is made of the problem of an interface crack with a contact zone. It is shown that the unrealistic oscillatory singularities are removed independent of the contact zone size. The model of Comninou [1, 2, 3, 4] leads to an equation for the contact zone length with possibly an infinity of solutions. However, only the largest of these appears to satisfy all the subsidiary conditions of the problem posed i.e. that of a single contact region. The singular shear stress field at the crack tip is effectively independent of the precise (small) contact zone length. An alternative model, illustrated in Fig. 3, is suggested. Each of these models leads to the same energy release rate.

Influence of Dwell Time on the Adherence of Elastomers

Abstract: We have studied the influence of the time of application of a given force, pressing a rigid spherical punch against a viscoelastic solid, on the kinetics of detachment when a known tensile force is applied suddenly. The edge of the contact surface is treated as a crack tip propagating in mode I at the interface between the two solids. It is shown that the general kinetics equation proposed earlier, G - w = wo(aTv), relating strain energy release rate G, Dupre's work of adhesion w, and the dissipation function o characteristic of the material tested, is confirmed provided that w is given higher values than those usually deduced from measurement of the contact area by the theory of adherence of elastic solids of Johnson et al. 21 It is found both that the time required for fracture varies with contact time (in direct proportion with t0.2 and that the work of adhesion varies directly with t0.1; this latter point means that the increase in adherence cannot be attributed to the diffusion of the free e...

The Growth of Impact Damage in Compressively Loaded Laminates

Abstract: The thesis is divided into two chapters. The first chapter describes an experimental program carried out to determine the phenomenological aspects of composite panel failure (graphite/epoxy laminate) under simultaneous in-plane compression and low velocity transverse impact (0-250 ft/sec). High-speed photography and the shadow moire technique were used to record a full-field surface deformation history of the impacted plate. The information gained from these records, supplemented by plate sectioning and observation for interior damage, has shown that the predominant failure mechanism is the coupled effect of delamination and buckling. In chapter 2, this process of failure is modelled by delamination buckling wherein the local delamination stability, growth or arrest are governed by an energy release rate criterion. Various degrees of problem simplifications are employed, starting with a one-dimensional, delaminated-beam model. In the most sophisticated treatment, it is assumed that the damaged area has an elliptical shape. It was found that this model is capable of describing the growth conditions and the growth behavior of the damaged area. It was also found that the predominant parameter controlling delamination growth or arrest is the fracture energy associated with delamination. In the appendix at the end of this work, the fracture energy of a composite laminate is considered. A modified cleavage analysis is developed, and is applied to evaluate this quantity for two composite materials of current interest. The test results are then examined with reference to impact damage tolerance data available for these materials. A viscoelastic characterization of the two resins used to fabricate the two composites mentioned above is also provided. The results of these measurements are then examined with reference to long-term applicability of the matrix material.

A simple test for the interlaminar fracture toughness of composites

Abstract: A simple test method for the measurement of delamination resistance is assessed through its application to 11-ply graphite-epoxy laminates whose matrices employ the F185 and 205 resins. The F185 resin has the same base epoxy as the 205, to which liquid and solid elastomers have been added. The critical value of the mixed mode energy release rate, calculated from a closed form equation employing nominal strain measurements from the onset of edge delamination, show that addition of the elastomers to the base epoxy increases interlaminar fracture toughness. Comparison of these results with those of width-tapered double cantilever beam (WTDCB) test data for the two materials shows a similar strain energy release rate, establishing the accuracy of the novel method. Both tests are found to be needed, however, for the quantitative characterization of interlaminar fracture toughness.

Characterization of Matrix/Interface-Controlled Strength of Unidirectional Composites

Abstract: This paper presents a method of characterizing the matrix/interface-controlled strength, including scatter, of unidirectional composites under combined loading. The failure envelope is represented by a second order polynomial and the scatter is described by the strength vector whose magnitude has a Weibull distribution. The method is based on the assumption of failure originating at inherent cracks parallel to the fibers and holds promise as a means of accounting for the size effect under combined loading. In addition, the energy release rate approach is discussed as a physical model and the appropriate data are presented.

The Relationship of Stiffness Changes in Composite Laminates to Fracture-Related Damage Mechanisms

Abstract: The monotonic or cyclic loading of continuous fiber laminated composite materials produces various types of micro-damage prior to fracture. Each time one of these micro-events occurs, the local and global stiffness of the material is altered, causing several types of variations in the tensor modulus components of the laminae and laminate. This paper attempts to establish specific relationships between these variations in stiffness and the factors which control the laminate fracture event.

Fatigue crack growth and fracture in glass sphere-filled nylon 6

Abstract: The common degrading effect of glass beads on the static fracture energy and the fatigue crack propagation response in nylon 6 materials is examined by conducting fracture mechanics tests and by considering the progress of cracks through the composites. The scanning electron micrographs indicate that the cracks travel through regions of polymer matrix and also along the interfaces between polymer and glass beads. It is demonstrated that, although fracture of the polymer regions requires considerable energy, cracking of the interfaces usually absorbs very little. Thus, the crack propagation is preferably concentrated on these microstructural regions, which is the cause of the decrease in fracture energy and increase in fatigue crack growth rate with increasing amount of glass spheres in the composite. Partial properties of the matrix and the interface are introduced in order to describe the fracture behavior and to improve the understanding of the gross fracture processes. The combination of these partial properties with the volume fraction of filler and certain geometrical factors by a modified rule of mixture leads to critical values for the failure of the composites, which are in reasonable accord with the measured fatigue and fracture data.

Applications of energy-release-rate techniques to part-through cracks in experimental pressure vessels

Abstract: In nonlinear applications of computational fracture mechanics, energy release rate techniques are used increasingly for computing stress intensity parameters of crack configurations. Recently, deLorenzi used the virtual-crack-extension method to derive an analytical expression for the energy release rate that is better suited for three-dimensional calculations than the well-known J-integral. Certain studies of fracture phenomena, such as pressurized-thermal-shock of cracked structures, require that crack tip parameters be determined for combined thermal and mechanical loads. A method is proposed here that modifies the isothermal formulation of deLorenzi to account for thermal strains in cracked bodies. This combined thermo-mechanical formulation of the energy release rate is valid for general fracture, including nonplanar fracture, and applies to thermo-elastic as well as deformation plasticity material models. Two applications of the technique are described here. In the first, semi-elliptical surface cracks in an experimental test vessel are analyzed under elastic-plastic conditions using the finite element method. The second application is a thick-walled test vessel subjected to combined pressure and thermal shock loadings.

Fracture mechanics of composites in compression along cracks

Abstract: Thus, based on the concepts in [5–7], the beginning of fracture of a composite in compression along a plane containing cracks can be represented as follows. If the material has not fractured already, then local fracture necessarily occurs next to the cracks at a value of compressive load corresponding to surface instability. Here, the upper limit of the ultimate theoretical strength corresponds to the minimum value of the shear modulus. This fracture mechanism can be seen in composites reinforced with high-modulus fibers. It should be noted that fracture can also take place on free surfaces of the material at these load values as a result of surface instability [1]. If the area of the free surface (lateral surface) of the material is substantially less than the total area of the cracks present throughout the volume of the material, then obviously the cracks will be the deciding factor in the fracture mechanism. The above-noted conclusions and quantitative abalysis were made only for a linearly elastic, orthotropic material with a high shear stiffness (brittle fracture), while the general results obtained in the present article also pertain to nonlinearly elastopiastic models. The results can be refined for more complex models. It must also be noted that the theoretical ultimate strength may be reduced substantially if the interaction of cracks located in parallel planes during instability is considered. This feature of the fracture mechanism was noted in note 6 in the article [6]. Composite materials generally have a fairly large number of cracks in planes and surfaces along the reinforcing elements. In connection with this, for composites it is best to allow for interaction of cracks located in parallel planes, which in turn should lead to a substantial reduction in the theoretical ultimate strength value obtained in the present article.

An application of M-integral to cracks in dissimilar elastic materials

Abstract: Here W is the strain energy density, n. is the unit normal to curve C, and u. is displacement vector. T. ~s the traction acting on C. It was foun~ by Smelser and Gurtin [5] ~hat the M-integral conservation law holds likewise for dissimilar materials whose interfaces lie along radial lines of the coordinate system chosen. By combining these results Nachman et al. [6,7] gave an expression of energy release rate for an edge crack along the interface between two elastic wedges with different elastic properties subjected to point loads at the apex. The author has independently examined the applicability of M-integral to energy release rate calculation in dissimilar materials and obtained some closed form expressions of energy release rates for other types of cracks.

Double torsion fracture toughness test for evaluating transverse cracking in composites

Abstract: An important failure mode of composite laminates is transverse cracking in the plies as a result of an applied load perpendicular to the fibre direction. This is a matrix-dominated mode. Transverse cracking in a composite can take place at loads below the failure load of the fibres. The damage sometimes leads to catastrophic failure and to property degradation of the laminates. A better understanding of this failure mode is particularly desirable. There has been a fair amount of work [1-7] on the mechanical behaviour of transverse cracking. It has been shown that the transverse crack process is controlled by the fracture toughness, defined by the critical strain energy release rate Gc, associated with this type of failure. The measurement of G e provides basic information about the transverse crack resistance of the laminates. In addition, it provides the materials scientist with an index for selecting resin matrix materials for composites to better resist transverse cracking. There are numerous test methods for measuring the fracture toughness of composite laminates. Most of them are based on tests originally used for homogeneous materials. The application of these techniques to angle-ply and cross-ply composites has not been all that satisfactory because of the complex damage phenomena involved. These composites do not usually fail with a single crack as is usually the case with homogeneous materials. Different methods have been developed to test laminates for transverse cracking parallel to the fibres. For example, Sanford and Stonesifer [8] used double edge notched (DEN) and single edge notched (SEN) specimens for evaluating the fracture toughness of (0 °) fibreglass laminates. Parvizi et al. [5] also used DEN and notched three point bend specimens for fracture toughness measurement on (0 °) fibreglass laminates. Slepetz and Carlson [9] employed compact tension specimens to test (0 °) S-glass/epoxy and (0 °) graphite/epoxy composites. The compliance calibration technique has been most conveniently employed for measuring the Gc of composites. The specimen compliance, C, against crack length, a, relationship is first established. In order to obtain an accurate C-a curve, a large enough population of specimens must be tested. In this respect, a test method which yields a linear C-a relationship is certainly more convenient to use, for example, the double torsion (DT) test [10, 11 ]. In addition to the advantage of rapid calibration of the C-a relationship, the test requires very simple specimen geometries which greatly minimize the machining operation involved. In this study, the double torsion test was investigated for its applicability to characterize transverse cracking in unidirectional fibre composites. This method has been successful for measuring fracture toughness of brittle homogeneous materials such as glass [10], ceramics [11] and glassy polymers [12-14]. When the technique was applied here to laminates, the load-displacement curves of the specimens were found to be different from those of the homogeneous materials. A correct interpretation of the results, however, led to the determination of meaningful fracture toughness related to transverse cracking. The original double torsion test technique was suggested by Outwater and developed by Kies and Clark [10]. The specimen is a rectangular plate supported along its two longer edges. In our case, the fibre direction was along the longer axis of the specimen. The specimen can be supported by either two rollers (Fig. 1) [11-14] or four steel spheres [15, 16]. In this study, we have experimented with test fixtures built with both of these supporting conditions. The load was applied to the specimen through two steel spheres as shown in Fig. 1.

Damage accumulation and fracture life in high-temperature low-cycle fatigue

Abstract: An analysis of the interaction of creep and fatigue is made based on the energy expended for the nucleation of damage at the advancing crack front. A rate equation is assumed for the damage nucleation, and the activation energy is taken as a function of the total mechanical energy at the crack tip. The analysis yields a relation in terms of J-integral which is applicable to both crack propagation and final failure. Raw data from various sources have been analyzed for different types of loading and compared with the theoretical prediction. The total energy in tension, which includes the tension-going strain rate, appears to be a good parameter for the prediction of fracture life in creep-fatigue interaction.

On the energy balance approach to fracture in creeping materials

Abstract: A continuum energy balance approach to the fracture of creeping materials is investigated in detail. Linear viscoelastic materials are considered and a non-linear stress dependence is introduced in order to describe the creep behaviour of metals at elevated temperatures. for linear materials energy balance considerations lead to a fracture criterion of the classical Griffith form. If such materials are incapable of storing strain energy (e.g. Young's modulus E → ∞) then fracture is impossible.

Applications of energy release rate techniques to part-through cracks in plates and cylinders. Volume 1. ORMGEN-3D: a finite element mesh generator for 3-dimensional crack geometries

Abstract: This report (Volume 1) describes the ORMGEN-3D (Oak Ridge Mesh GENerator - 3D) finite element mesh generator program for computational fracture mechanics analysis. The program automatically generates a three-dimensional (3-D) finite element model for six different crack geometries. These geometries include flat plates with straight or curved surface cracks and cylinders with part-through cracks on the outer or inner surface. Mathematical or user-defined crack shapes may be considered. ORMGEN-3D generates a core of special wedge or collapsed prism elements at the crack front to introduce the appropriate stress singularity at the crack tip. Regular 20-node isoparametric brick elements are used elsewhere in the modeling. Also, a cladding option is available that allows for an embedded or penetrating crack in the clad material. As few as four input cards are required to execute the program. ORMGEN-3D is part of a three-program system, ORMGEN-ADINA-ORVIRT, which addresses linear or nonlinear fracture in 2- or 3-D crack geometries.

Experimental studies of the fibre pull-out problem

Abstract: The fibre pull-out problem was studied experimentally using a method which enabled direct measurement of the energy release rate of de-bond and also observation of the fracture process involved. Preliminary test results indicated that the process was a twostage one, with de-bond initiating at the fibre tip, followed later by de-bond initiating at the free surface end. If a flaw of sufficient size was present then a stage-two de-bond would occur. Results showed reasonable agreement between experimental results and computer measurements.

Fracture Mechanics of Delamination. Initiation and Growth.

Abstract: : This report describes the results from an experimental and analytical study on the fracture mechanics of delamination. Experiments have been conducted using the AS-3501-06 graphite-epoxy laminates in order to observe delamination growth of various geometrical and loading conditions. Static and fatigue crack growth under both tension and compressive loads are studied. The experiments helped to identify and isolate the most important loading, geometry and material parameters which influence the delamination processes. Predictive models are then developed to model these processes, based on the linear elastic fracture mechanics concept of energy release rate. The models are executed by a finite element routine which simulates the crack growth process. Extension of the energy method to the growth process under constant amplitude fatigue loads leads to the concept of constant damage states. This concept is readily applied in a cumulative damage model for fatigue under spectrum loading. (Author)

Determination of stress intensity factors

Abstract: The application of fracture mechanics principles bears largely upon the stress intensity factor. An essential part of the solution of a fracture problem in linear elastic fracture mechanics is the establishment of the stress intensity factor for the crack problem under consideration. Since the introduction of fracture mechanics much effort has been put into the derivation of stress intensity factors, and a variety of methods have been developed to approach the problem.

Model for fracture toughness alteration due to cyclic loading

Abstract: A new model that is capable of predicting and explaining the effect of cyclic loading on the apparent fracture toughness of materials was developed. The model combines macroscopic fracture criteria with the assumption that transient flow properties of material in the cyclic plastic zone can be simulated by those of macroscopic low cycle fatigue specimens, tested in reversed strain control. Little or no changes in the cleavage fracture toughness due to cyclic loading is predicted or observed for materials that cycle strain harden (e.g., rail steel) and in the fracture toughness of other materials that cycle strain harden (e.g., the commercial 2000 series Al-Cu alloys) and fracture by rupture. However, an increase in the fracture toughness is predicted and observed for materials that cycle strain soften (e.g., 1Cr-Mo-V and 18 Ni 300 maraging steels), irrespective of fracture mode (cleavage or rupture). The changes in the fracture toughness are predicted and observed to increase with both the number of cycles of applied load and the reversed plastic strain range (or stress intensity range for precracked specimens).

The energy principle

Abstract: The Griffith energy criterion for fracture [1, 2] states: crack growth can occur if the energy required to form an additional crack of size da can just be delivered by the system. The case of a plate with fixed ends was discussed in chapter 1. Due to the fixed ends the external load cannot do work. The energy required for crack growth must then be delivered as a release of elastic energy. If the ends of the plate are free to move during crack extension, work is done by the external load. In this case the elastic energy content of the plate increases instead of decreasing.

A Fundamental Research on the Growth Pattern of Cracks

Abstract: In order to obtain the precise failure process of structures, the importance has recently been recognized for the crack growth path of structures under tensile loading conditions. Several criteria had been proposed for the determination of the crack growth direction, i. e. the criteria of maximum hoop stress, minimum strain energy density, locally symmetric deformation, and maximum energy release rate. Using these criteria the finite initial branch angle of the crack growth can be predicted, if the stress intensity factor of the in-plane shear mode, KII, exists at the pre-existing crack tip.The abrupt crack curving is, however, often observed even if KII≅0 at the crack tip, where severe bending or biaxial stress condition holds. Recently Cotterell and Rice examined this problem, and proposed the T-stress theory by using a small perturbation technique, in which they introduced the concept of stability for the crack growth path. T-stress is defined as the constant component of the normal stress acting parallel to the crack line, when the near tip stress field is expanded in terms of the distance from the crack tip. In their theory, if T>0, the crack growth path is unstable, i. e. the abrupt crack curving is expected, and vice versa. In case of biaxially stressed plate, this theory is successful in predicting the crack path stability, while the crack path is stable for the compact-tension specimen even though the T-stress is positive. Therefore the generality of the theory is still open to question.In the present paper, based upon the crack path prediction obtained in the first report, the authors introduce the concept of intermediate range of stability for the crack growth path. This stability concept includes the length parameter corresponding to the crack growth, while only the immediate range of stability is considered by the theory of Cotterell and Rice. Numerical calculations are performed by using the finite element method, and the stability of the present theory is determined for various stress conditions at the crack tip. The numerical results clarify the difference of the present and Cotterell-Rice theories, and also confirm the stable crack growth path for the compact-tension type specimen.Finally experiments are performed for the cases corresponding to the numerical calculations. The test specimens, which are made of PMMA, are prepared, and quasi-statically fractured under the monotonically increasing displacement with practically Mode I loading conditions. Various stable and unstable crack growth paths are observed, and the theoretical prediction of the stability for the crack growth path agrees quite well with the experimental results.