Cohesive theories of fracture are applied to simulate the complex failure modes in sandwich structures subjected to low-speed impact. The particular configuration contemplated in this study refers to the experiments performed by Xu and Rosakis [1], where the model specimens involving a compliant polymer core sandwiched between two metal layers, were adopted to simulate failure evolution mechanisms in real sandwich structures. Fracture has been modeled by recourse to an irreversible cohesive law embedded into three-dimensional cohesive elements. These cohesive elements govern all aspects of the separation of the incipient cracks. The cohesive behavior of the material is assumed to be rate independent and, consequently, all rate effects predicted by the calculations are due to inertia. The fidelity of the model has been validated by several previous simulations [2,3]. The numerical simulations have proved highly predictive of a number of observed features, including: the complex sequences of the failure mode, shear-dominated inter-sonic (a speed that is greater than shear wave speed but less than the longitudinal wave speed of the material) inter-layer cracks, the transition from inter-layer crack growth to intra-layer crack formation and the core branching later on.
This paper develops a damage model for the evaluation of low cycle fatigue lives under complex cyclic multiaxial loadings. One of the authors has proposed the equivalent strain parameter for the life prediction of the nonproportional low cycle fatigue. This strain parameter can evaluate the dependence of fatigue lives on strain history and material, and correlates the fatigue lives within a small scatter band for 15 kinds of proportional and nonproportional strain paths. However, the parameter was only applicable to the life prediction under a limited nonproportional strain history, so that some modifications were required. In this study, a simple damage model for the life prediction is proposed by combining the equivalent strain parameter with Miner's law in order to apply it to the life prediction under more complex nonproportional loadings. The applicability of the proposed model is examined for the life evaluation of nonproportional low cycle fatigue for different materials; type 304 stainless steels, copper, aluminum alloys, chromium-molybdenum and carbon steels, which were obtained from different research institutes. The model can correlate most of the fatigue data within a factor of two scatter band and has a potential to become a good damage model for nonproportional low cycle fatigue.
A stability analysis is presented for circumferential cracks of constant depth in cantilevered pipings. The analysis is based on the tearing modulus concept and the tearing stability criterion. Assuming that the cracked cross-section is subjected to limit moment the crack growth is studied in the case of pipings subjected to impact loading.
In the present paper the Boundary Finite Element Method is presented as a boundary discretization method for the numerical investigation of interfacial stress concentrations in composite laminates. In contrast to the classical boundary element method, the element formulation is finite element based, which avoids the necessity of a fundamental solution. Comparative results from finite element calculations show good agreement both for the laminate free-edge effect and for the example of the stress concentrations near cracks in composite laminates.
This paper reports the results of research studies on measuring the mode II fracture toughness, GIIC, of structural adhesive joints via a Linear Elastic Fracture Mechanics (LEFM) test method. Adhesive joints were manufactured using carbon-fibre reinforced plastic substrates and these were bonded with one of two commercial structural epoxy adhesives. Mode II loading was achieved using the end-loaded split test geometry and the specimen dimensions were controlled to ensure the conditions of LEFM were not violated. Data analysis was achieved by the use of corrected beam theory and experimental compliances approaches. Values of GIIC were plotted against the measured crack length to yield the apparent mode II resistance curves (i.e. the mode II R-curves). These curves revealed a characteristic shape that required detailed interpretation. Uncertainties in the measured crack length values were identified as the most likely cause of the disagreement between the values of GIIC deduced via corrected beam theory and experimental compliance approaches. It is suggested that these uncertainties are due to the problem of misinterpreting microcracking as the main crack growing.
Notched specimens of polyethylene (PE) have been subjected to constant and cyclic loading at 80 Cdegrees, and their microde formation behaviour investigated by OM, SEM and TEM. Under constant loading, a transition from full ligament yielding to slow crack growth (SCG) was observed as the stress intensity factor, K, decreased, reflected by a macroscopic ductile-brittle transition with decreasing applied load. SCG was characterized by formation of a wedge-shaped crack tip deformation zone, whose internal structure became progressively finer as K decreased further. The behaviour of relatively SCG resistant third and second generation grades of PE in the low K limit was inferred from TEM of specimens subjected to accelerated testing in Igepal(TM) to be breakdown of diffuse zones of interlamellar voiding rather than development of a mature fibrillar structure. This latter failure mode gave smooth fracture surfaces, similar to those observed under conditions, which have been linked to a transition from discontinuous (stick-slip) crack growth to continuous crack growth with decreasing peak K. TEM again indicated the smooth fracture surfaces obtained under low level cyclic loading conditions to be associated with breakdown of regions of interlamellar voiding, suggesting the micromechanisms of failure to be similar in both types of accelerated test. On the other hand, at higher K, crack advance under dynamic loading led to more extensive fibrillar retraction than for static loading.
Fixed arm peel and T-peel test procedures are used to measure peel strength for flexible laminates. Analysis of the contributions from elastic and plastic deformations of the peel arms during these tests enables the energy contribution from plastic effects to be subtracted from the energy required to peel the laminate. In this way, the adhesive fracture toughness is determined.Seven independent laboratories have conducted these procedures (through the ESIS TC4 group) on a flexible polypropylene laminate system. Experiments for fixed arm peel have been conducted at a common peel angle (900) and also for multiple angles (60degrees-160degrees) in order to determine the adhesive fracture toughness. These laboratories also conducted measurements with a T-peel geometry. Similar values were obtained for the adhesive fracture toughness demonstrating that with careful thought to the various energy contributions in the peel tests that a geometry independent value can be derived.The corrections for plastic deformation have been further analysed for metallic substrate laminates, using these two test geometries. A method is suggested for monitoring the correction. It is believed that corrections up to about 70% can be accommodated by the test protocols. Moreover, by investigating the temperature dependence of adhesive fracture toughness for the metallic substrate system, even larger plastic corrections may be tackled (greater than 80%). However, the accuracy of the ensuing results becomes more doubtful.
The fracture behaviour at low strain rates of "amorphous" injection moulded Poly(Ethylene-Terephthalate) (PET) samples (< 6% crystallinity) and its blends with Bisphenol A Polycarbonate (PC) were studied by the Essential Work of Fracture (EWF) method and the Ferrer-Balas partitioning methodology. The effect of specimen orientation, testing rate and PC content were investigated. In PET samples, at the same testing rate, w(e) is slightly lower while betaw(p) is higher, when crack propagation occurs in the melt flow direction, as previously reported. Additionally, a decreasing trend in w(e), with testing rate was observed, which seems to be related to the restriction of some deformation processes at the propagation stage as the partitioning method reveals. In the case of PET/PC blends, where evidence of transesterification during melt blending have been verified, as the PC content increases, lower values of the EWF parameters were obtained for transverse-to-flow crack propagation. This trend, unlike the parallel-to-flow situation, seems to be dictated by deformation processes involved at crack initiation. In general, while at lower PC content the fracture behaviour is mainly controlled by transesterification effects, at higher content the oriented and stratified morphology which is developed seems to control the fracture behaviour.
Whether a pressurized structure will leak or burst when suddenly cracked depends on the material’s resistance to rapid crack propagation and its ability to arrest a crack. Thus, the governing material property, namely the stress intensity-crack velocity relationship, is necessary input for designing pressurized pipes and vessels and establishing safe operating conditions. Unfortunately, this material property is not easily measured, and reliable data do not generally exist. This paper describes and presents results from rapid fracture experiments on polymethyl methacrylate (PMMA) compact tension specimens and analyzes published data from other specimen geometries. After a certain propagation distance, the stress intensity at a fast moving crack front, KID, is governed by the initial stress intensity, KQ, and the dynamic response of the specimen. A plot relating KID/KQ to normalized crack length, a/W, unifies the RCP test data and defines a master curve for the specific specimen geometry. The results suggest a practical and simple method for measuring toughnesses associated with rapidly running and arresting cracks, and hence a route for managing catastrophic failure of pressurized structures.
Results are reported from an investigation into the geometrical aspects of multiaxial fatigue using a newly developed method for testing of rhombic specimens. The new method is used to obtain biaxial stress by applying simultaneously reversed tension and compression bending in perpendicular directions to a rectangular plate (anticlastic bending). Constant-load amplitude fatigue tests of aluminium alloy 2024 T351 specimens were conducted at several load levels. The specimen's critical surface and subsurface strains and stresses were evaluated by using a 3D elastic-plastic finite element analysis (FEA). Results from the numerical simulation indicated that the critical maximum shear strain plane is both geometrically and loading dependent. A fair prediction of the specimens' life is obtained by using the material data, the simulated maximum shear strains and a subsurface strain damage model. The experimental and the predicted results are discussed, and further development of the subsurface strain model is presented.
Standard small-scale peel tests, such as the impact wedge-peel (IWP-ISO 11343) and T-peel tests are often employed to analyse the fracture behaviour of structural adhesives. The current work aims to examine the behaviour of adhesively bonded joints under various loading rates by conducting a series of peel tests and simulating the results from such tests numerically. In all tests, thin sheets of aluminium alloy substrates were bonded together using 'XD4600' and 'XD1493' structural epoxy-adhesives. Numerical modelling of the tests was conducted using the Finite Volume (FV) method. For this purpose, transient, 3D, procedures were developed including a newly developed contact model and a cohesive zone (CZ) model as a local failure criterion. The CZ model was defined using two materials parameters, the adhesive fracture energy, G(c), and the maximum cohesive stress, sigma(m). In order to measure the adhesive fracture energy tapered double cantilever beam (TDCB) tests were per-formed, whereas the value of sigma(m) was estimated from the stress-strain curves at corresponding rates and taken to be the ultimate tensile strength (UTS). Numerical analysis of the tests was conducted in order to calibrate the traction separation curves at various rates, and to examine the stick-slip crack behaviour which appeared in TDCB specimens with 'XD4600' adhesive tested at high rates. The calibrated CZ curves were then used in the prediction of failures in the IWP specimens. Work on modelling T-peel tests is currently in progress.
A high-throughput combinatorial approach to edge delamination test is proposed to map the failure of adhesion as a function of both temperature and film thickness in a single step. In this approach, a single specimen of a thin film bonded to a substrate with orthogonal thickness and temperature gradients is subdivided into separate samples. This approach can be adopted to measure the adhesion for films with thickness in the sub-micron range by the addition of an overlayer. Requirements for valid testing results from a mechanistic viewpoint are analyzed using three-dimensional computational fracture mechanics. An initial test result is presented to demonstrate the feasibility of the approach.
In order to investigate the cause of the microcrack branching instability observed by Fineberg, Gross, Marder and Swinney (1992, Phys. Rev. B45, 5146), we have calculated the stress fields at the tip of dynamic mode-I crack associated with the sound waves which form the standing waves across the elastic plate of PMMA (polymethyl-methacrylate) and modulate the stress intensity factor, K-I, of the crack as, SigmaK(I)C(I)((n))cos(omegat-beta(x)x)cosbeta(n)z, where C-I((n)) is the amplitude of modulation. The quantity, omega, is the angular frequency of the waves. The quantities, beta(x) and beta(n), are the wavenumbers in x and z-direction, respectively. The crack propagates in x-direction along the plane, y=0. The boundary condition for the singular stress field, sigma(zz)((0)) = 0, at the plate surfaces, z=+/-w/2, determines the quantity, beta(n), by the equation, cosbeta(n)w/2=0. The boundary conditions at the plate surfaces for the 1-st order stress fields, sigma(xz)((1))=sigma(yz)((1))=0, give the following equation, Sigmabeta(n)rC(I)((n)) sin(n+0.5)pi=0, where n is the integer and r, the distance from the crack tip. Combining this equation with the normalization condition of the modulation amplitude, SigmaC(I)((n))=1, we find that the interference patterns of the stress fields at the crack tip associated with the standing waves across the plate are enhanced by the order of magnitude depending on the choice of the mode numbers of the standing waves. The possible effect of this result on the microcrack branching instability is discussed.
This paper is concerned with the fracture of glassy polymers at high loading rates, where thermal effects due to self-heating of the material can become important. A coupled thermomechanical, small-scale yielding calculation is performed that incorporates a recent cohesive zone model for crazing while a viscoplastic model is used to describe shear yielding. When crazing takes place, this mechanism is identified as the major heat source for the temperature increase while the conversion of bulk viscoplasticity to heat appears to be negligible. At sufficiently high remote loading rates, the glass transition temperature can be reached next to the craze but the hot zone is too small to promote thermal blunting by large plastic deformations near the crack tip. Since crack growth is caused by craze breakdown, the evolution of the toughness with increasing loading rate is primarily governed by the craze properties. Their rate dependence can partially explain the brittle to ductile transition.
The experiments described herein were performed to determine whether damage imposed by axial loading interacts with damage imposed by torsional loading. This paper is a follow on to a study [1] that investigated effects of load-type sequencing on the cumulative fatigue behavior of a cobalt base superalloy, Haynes 188, at 538degreesC. Both the current and the previous study were used to test the applicability of cumulative fatigue damage models to conditions where damage is imposed by different loading modes. In the previous study, axial and torsional two load level cumulative fatigue experiments were conducted, in varied combinations, with the low-cycle fatigue (high amplitude loading) applied first. In present study, the low amplitude fatigue loading was applied initially. As in the previous study, four sequences (axial/axial, torsion/torsion, axial/torsion, and torsion/axial) of two load level cumulative fatigue experiments were performed. The amount of fatigue damage contributed by each of the imposed loads was estimated by both the Palmgren-Miner linear damage rule (LDR) and the non-linear, damage curve approach (DCA). Life predictions for the various cumulative loading combinations are compared with experimental results. Unlike the previous study where the DCA proved markedly superior, no clear advantage can be discerned for either of the cumulative fatigue damage models for the loading sequences performed. In addition, the cyclic deformation behavior under the various combinations of loading is presented.
This paper describes the use of an instrumented drop tower to perform high strain rate fracture testing of polymers using a method previously described by Williams [1] and Rager [2]. This is being investigated by Technical Committee 4 of the European Structural Integrity Society (ESIS) as a possible future test standard. The method utilises a high rate test on a single edge notched bend test (SENB) specimen, from which fracture toughness parameters are determined by analysis based on time to failure. Tests were conducted on three polymers PVC, PE and PMMA at impact speeds in the range 1 ms(-1) to 16 ms(-1). Contact stiffness was measured at similar impact speeds using a similar geometry striker against fully supported specimens. Dynamic elastic moduli were also measured in compression tests by longitudinal compression using similar geometry but un notched samples from the same materials batch. Tests were also monitored by high-speed video in order to provide crack tip velocity data and to confirm the nature of the fracture process. Finally a comparison is made between the dynamic key curve analysis and mass spring model analysis for to determine dynamic fracture toughness.
It is well known that polyethylene, although tough when stressed in air, becomes brittle in the presence of some specific substances, among which are non-ionic detergent-water solutions. In this work two polyethylenes, obtained with two different catalytic systems, were considered. Fracture behaviour was examined in air and in the presence of a stress-cracking agent (a water/Antarox CO-630 solution) at 50 degreesC, for both polyethylenes. The effect of detergent concentration in water was then investigated for one of the two materials.Fracture tests were performed on single edge notched specimens, in four point bending under constant load (creep). The results show that the fracture behaviour of the two materials is qualitatively very similar, although the fracture resistance levels are different. In the presence of the stress cracking agent it was observed that there is a critical value of the applied stress intensity factor, different for the two materials, above which the detergent does not seem to have any effect on fracture initiation time nor on crack propagation rate. Below this value, however, the environmental stress-cracking agent accelerates fracture initiation. The concentration of the detergent in water on fracture behaviour affects both crack initiation and propagation, the stronger effect occurring for a value around 50%.The results are discussed in terms of material and stress-cracking agent characteristics, and their interactions.
The fracture toughness of a polymer-metal laminate composite is obtained by mechanical testing of a specimen containing a pre-crack. The laminate is a material used for packaging. It consists of a thin aluminium foil and a polymer coating. A centre cracked panel test geometry is used. Each of the layers forming the laminate is also tested separately. The result is compared with the measured fracture strength of the individual layers. It is observed that the load carrying capacity increases dramatically for the laminate. At the strain when peak load is reached for the laminate only aluminium is expected to carry any substantial load because of the low stiffness of the LDPE. However, the strength of the laminate is almost twice the strength of the aluminium foil. The reason seems to be that the aluminium forces the polymer to absorb large quantities of energy at small nominal strain. The toughness compares well with the accumulated toughness of all involved layers. Possible fracture of the interface between the layers is discussed.
The fracture toughness of a semi-crystalline polymer (PP) filled with mineral submicron and micron scale particles is investigated according to the J-integral method: determination of the crack initiation energy (J(C)), and the crack propagation resistance dJ/d(Deltaa). Ultrafine mineral particles as precipitated silica (aggregate particle size < 0.1 mum) strongly affect the viscoelastic properties of the PP matrix, with an increase of the elastic modulus. Mineral particles with surface treatment or larger diameter size (> 1 mum), lead to an improvement of the PP fracture toughness by induced local debonding mechanism. Debonding with void growth is the main mechanism to allow dissipation energy in these mineral filled materials: debonding process is controlled by the local stress at particle/matrix interface and the adhesion energy. A synergy effect is obtained by association of calcium carbonate CaCO3 (> 1 mum) and ultrafine silica SiO2 particles (< 0.1 mum) : the behaviour of PP/ 2% SiO2/ 5% CaCO3 composites is considerably improved, with both high fracture toughness value and a high elastic modulus. The combination of ultrafine and larger mineral particles leads to an increase of both the process zone size ahead of the main propagating crack and energy density dissipated in this process zone. The dispersion of multi-scale mineral particles is a new way to develop significantly improved mechanical behaviour of polymers, specially elastic modulus with high fracture toughness.
Cracks inside polymeric packaging materials, which are used for protection against environmental impacts and isolation of electronic components, can lead to failure of the whole system. Therefore the understanding of crack initiation and propagation becomes vital for the design of reliable microsystems. In this paper the loading situation of cracks inside the polymer is analysed considering an encapsulated metal structure. The analysis is based on finite element simulations of thermally induced stresses, where rate-dependent material behaviour is being taken into account. Different fracture criteria like Schapery's Work of Fracture, the modified virtual crack closure integral (MCCI), the path independent J-Integral, and the stress intensity factor are being compared and evaluated with respect to their applicability to thermomechanical loading situations (cooling). A good agreement with experimental results is achieved, when the actual load K-I, loading speed dK(I)/dt and temperature is used to describe critical loading situations. The obtained results are applied to the analysis of a demonstrator. Elastic and viscoelastic simulations are compared and effects of loading rate are investigated. Thus a methodology is being illustrated which enables the consideration of rate dependent material behaviour in a fracture mechanical analysis under thermomechanical loading.
