A local modulus analysis of rapid crack propagation in polymers

This work is concerned with the analysis of rapid crack propagation (RCP) in Polymethylmethacrylate (PMMA), Polycarbonate (PC) and two-layer PMMA/PC systems. Remarkably constant crack speeds were observed, and higher crack speeds corresponded to the higher preloads. Uniform fracture surfaces were associated with these constant speed RCPs. An indirect method was used to characterise dynamic fracture properties of the materials. The method relies on the recorded crack length histories and boundary conditions which are incorporated in a dynamic Finite Element (FE) code to generate the crack resistance (G _ID). The numerical simulation of the constant speed RCPs generated highly scattered G _ID data. Very large variations of the computed G _ID with the crack length did not correspond to fracture surface appearances. Geometry dependent and multivalued crack resistance results with respect to the crack speed cast doubt on the uniqueness of G _ID. In this work, attempts were made to overcome these difficulties by exploring the concept that the anomalies arise from large local strains around the rapidly moving crack tip, resulting in the crack seeing a low local modulus. It is demonstrated that the critical source of error on the analysis of RCP, is the improper linear elastic representation of the material behaviour around the propagating crack tip. Since the parameters describing the behaviour of the materials near the propagating crack tip were unknown, local non-linear effects were approximated by a local low modulus strip along the prospective crack path. The choice of the local modulus was justified by measurements of the strain histories along the crack path during RCP. The local strip low modulus model generated a larger amount of the kinetic energy in the sample and the crack resistance was reduced compared to results from the single constant modulus approach. Most importantly, G _ID data were nearly independent of the crack length, crack speed and the specimen size. This local modulus concept was also successfully applied to the analysis of RCP in the duplex specimen configuration.     

Deformation and fracture of styrene-acrylonitril copolymer - rubber blends: Microscopy studies of deformation zones

A styrene-acrylonitril copolymer (SAN) was toughened by SAN-grafted polybutadiene core-shell rubber particles. Notched tensile specimens were fractured with a tensile speed ranging from 10-4 to 10 m s-1. The deformation processes close to the fracture surface were studied by means of transmission electron microscopy. A marked difference in the structure of the deformation zone was observed between low speed (10-3 m s-1) and high speed (≥1 m s-1) deformed samples. At low tensile speed the structure of the deformation zone correlated closely with fracture mechanics theory. When the tensile speed was increased the deformation zone had a layered structure. In the zone 400–1.5 μm below the fracture surface the deformation structure was similar to that at low speed. In the layer 1.5–0.5 μm from the fracture surface the rubber particles were strongly deformed, but no cavities or crazes could be observed. Directly next to the fracture surface the high speed deformation zone showed a small layer (0.5 μm) where all the deformation had vanished. It is suggested that due to high strain-rate plasticity at the crack tip a temperature rise occurs which is high enough to cause complete relaxation of the deformation in this layer. Therefore, locally the glass transition temperature of the matrix material was reached. The interaction between thermal effects and deformation processes at the crack tip is discussed. This revised version was published online in November 2006 with corrections to the Cover Date.     

Fracture energy of epoxy resin under plane strain conditions

The fracture behaviour of an epoxy resin has been studied by a method which involves the pressurization of an internal circular crack. The method can be used to study both cohesive fracture and the adhesive failure of an interface. Plane strain conditions are assured because the crack does not intersect a free surface and (for adhesive failure) shrinkage stresses are eliminated as a crack driving force. Using high speed photography, the dependence of crack speed on critical pressure and specimen geometry was determined. An elastic analysis permits the derivation of fracture energy as a function of crack velocity. Fracture energy values lay between 100 and 200 Jm^–3 at 35° C with a peak at a crack velocity of 37 m sec^–1.     

Quasi-static and dynamic fracture behaviour of rock materials: phenomena and mechanisms

An experimental investigation is conducted to study the quasi-static and dynamic fracture behaviour of sedimentary, igneous and metamorphic rocks. The notched semi-circular bending method has been employed to determine fracture parameters over a wide range of loading rates using both a servo-hydraulic machine and a split Hopkinson pressure bar. The time to fracture, crack speed and velocity of the flying fragment are measured by strain gauges, crack propagation gauge and high-speed photography on the macroscopic level. Dynamic crack initiation toughness is determined from the dynamic stress intensity factor at the time to fracture, and dynamic crack growth toughness is derived by the dynamic fracture energy at a specific crack speed. Systematic fractographic studies on fracture surface are carried out to examine the micromechanisms of fracture. This study reveals clearly that: (1) the crack initiation and growth toughness increase with increasing loading rate and crack speed; (2) the kinetic energy of the flying fragments increases with increasing striking speed; (3) the dynamic fracture energy increases rapidly with the increase of crack speed, and a semi-empirical rate-dependent model is proposed; and (4) the characteristics of fracture surface imply that the failure mechanisms depend on loading rate and rock microstructure.     

Experimental Determination of Dynamic Crack Initiation and Propagation Fracture Toughness in Thin Aluminum Sheets

An experimental investigation was undertaken to characterize the dynamic fracture characteristics of 2024-T3 aluminum thin sheets ranging in thickness from 1.63–2.54 mm. Specifically, the critical dynamic stress intensity factor Kdc was determined over a wide range of loading rates ( expressed as the time rate of change of the stress intensity factor KdI ) using both a servo- hydraulic loading frame and a split Hopkinson bar in tension. In addition, the dynamic crack propagation toughness, KD, was measured as a function of crack tip speed using high sensitivity strain gages. A dramatic increase in both Kdc and KD was observed with increasing loading rate and crack tip speed, respectively. These relations were found to be independent of specimen thickness over the range of 1.5 to 2.5 mm.     

Impact fracture of polyethylene: A non-linear-elastic thermal decohesion model

A model for brittle dynamic and impact fracture of tough polymers has recently been proposed, according to which a crack-tip Dugdale craze fails by melting of a thin layer at each cohesive surface. A plane-stress, linear-elastic formulation accounted for the measured dynamic fracture resistance to within the accuracy of measurement, and for the variation of impact fracture resistance with impact speed, in two pipe-grade polyethylenes; but the predicted impact fracture toughness G_c was in error by a factor of up to two. It is shown here that a pseudoelastic formulation, which accounts for non-linearity of the impact load/displacement trace due to craze extension as well as to non-linear elasticity, corrects these shortcomings. Impact fracture behaviour of a medium density and modified high-density polyethylene between −20 and 23°C, which embraces a transition to notch-ductile behaviour, is predicted using stress/strain and thermal property data only.     

Cyclic Crack Resistance of Grey and High-Strength Cast Irons with Increased Phosphorus Content

We investigated the influence of phosphorus (0.02–0.76%) on the microstructure, short-term strength, cyclic crack resistance characteristics, and micromechanism of fatigue fracture of grey and high-strength cast irons. It was established that the low cyclic crack resistance of grey and high-strength cast irons with increased phosphorus contents (0.7–0.8%) is caused by the propagation of a fatigue crack via intergranular cleavage, initiated by a discontinuous or continuous network of precipitates of the ternary fine-grained phosphide eutectic along boundaries of ferrite grains. We showed that, from the viewpoint of cyclic crack resistance, it is admissible to alloy cast irons of the ferritic and ferritic–pearlitic class with phosphorus up to 0.3% when the phosphide eutectic forms in amounts of 3–5% for grey cast irons and 4–7% for high-strength cast irons without significant decrease in their resistance to brittle fracture.     

An evaluation of double-torsion testing of polymers by visualization and recording of curved crack growth

The development and growth of the curved crack front in a double-torsion fracture-mechanics specimen is investigated by direct observation of crack propagation during the test. The crack front motion is analysed from a video-recording of the fracture test, and three distinct stages of crack propagation are identified. This work shows some of the requirements for the application of conventional double-torsion analysis to this test configuration: the material characteristic —critical strain energy release rate as a function of crack velocity — can be correctly obtained, provided that three steady-state conditions (static, kinematic and dynamic) are all fulfilled.     

Toughened polybutyleneterephthalate compounds

The notch sensitivity of polybutyleneterephthalate (PBT) had been improved in a synergistic way, by 30–40 times, by addition of special toughening agents in limited amounts (20–30%). This large toughening effect was studied by high speed photography. Ultimate elongation strain and strain rate at the notch root were measured directly. It was found that the high impact behaviour of toughened PBT is provided by the large amount of plastic strain around the fracture surface. The plastic strain was not observed in the PBT homopolymer during impact fracture, due to its brittle behaviour; on the contrary, it was observed in low speed bending of notched bars. It was concluded that the toughening mechanism of mixed additives is to allow the plastic strain of a PBT matrix at very high strain rates.Now Himont Italia.     

Fractographic study of high-density polyethylene pipe

High-density polyethylene (HDPE) pipe is now being used as an alternative to medium-density polyethylene (MDPE) for gas, water, sewage and waste-water distribution systems. Laboratory tests appear to show that HDPE is more able to suppress rapid crack propagation (RCP), whilst remaining sufficient resistance under the operational circumstances that lead to the type of slow crack growth observed in service failures. There have been many fractographic studies on MDPE pipe materials, actual pipe and fittings, but little on HDPE. A fractographic study of the type of HDPE pipe in current production has been undertaken. For these tests, whole pipe sections were subjected to either static or dynamic internal (water) pressurization fatigue loading. Failure mechanisms are discussed based on the fracture morphologies resulting from these tests. A further argument for good resistance of HDPE pipe to RCP is suggested. © 1998 Chapman & Hall     

A mechanism of crack branching in polymethyl methacrylate and the origin of the bands on the surfaces of fracture

At low crack velocities the fracture of high molecular weight polymethyl methacrylate occurs by the separation of a thin craze layer ahead of, and coplanar with, the propagating crack tip. Above some critical velocity, about 400 m sec^–1 at room temperature, craze branching or bifurcation is initiated. The craze branching does not cause any detectable surface roughening of the fracture surface until the crack tip stress is sufficient to initiate cracks in the craze branches. At this stage the formation of the branching craze-cracks causes surface roughening (bands or striations), a deceleration of the main fracture and a drop in the stress amplitude around the crack tip which is below that necessary to initiate branching crazes. The fracture then reverts back to the simpler mechanism, with no surface roughening. The repetition of this process gives rise to the banded appearance of the fracture surface.     

Effect of mono and composite coating on dynamic fracture toughness of metals at different temperatures

It is well known that during the operating condition of any metallic structural system the dynamic crack growth speed is in the order of 1–2 km/s. Industrial finishes like coating which form the integral part of manufacturing is adopted to improve fracture toughness of metals. These coated samples coated with thin films are mechanically tested by Charpy V-notch impact tester for estimating dynamic fracture toughness. Coatings improve the wear and corrosion resistance of materials; they tend to reduce the strength of materials, because of the increased residual stresses due to the coating process. Defects cannot be precluded from these coated and treated components; strength of those components in the presence of these defects can be analyzed by fracture mechanics approach. An attempt has been made to analyze the effectiveness of coating methods like electroplating, PVD (Physical Vapour Deposition), coating thickness and the service temperature on the fracture behaviour of metals. Experiments have been carried out on EN8 steel and aluminium for different temperatures and the later samples were corroded for 2400 h and tested for corrosion resistance. The specimen preparation and experimentations were carried out according to the ASTM standard E-23. Finite element analysis was done by FRANC 2D (Fracture Analysis Code) for estimating the stress intensity factor at different crack lengths along with influence of temperature and corrosion. PVD coated samples of Al–N (aluminium nitride) and nano-crystalline layer of Ti–Al–N (titanium aluminium nitride) showed improved dynamic fracture toughness properties. The same set of samples showed decrease in stress intensity factors and excellent corrosion resistance compared to conventional Ni (nickel) and Cr (chromium) coated samples. Mechanical behaviour of selected metals under heat affected zone is of also discussed in this paper, the study aims at both coated and uncoated cases. Performances of metals in cryogenic condition are also paid attention in this paper.     

Finite volume method and multigrid acceleration in modelling of rapid crack propagation in full-scale pipe test

Rapid Crack Propagation (RCP) along pressurised plastic pipes is by far the most dangerous pipe failure mode. Despite the economic benefits offered by increasing pipe size and operating pressure, both strategies increase the risk and the potential consequences of RCP. It is therefore extremely important to account for RCP in establishing the safe operational conditions. Combined experimental-numerical study is the only reliable approach of addressing the problem, and extensive research is undertaken by various fracture groups (e.g. Southwest Research Institute – USA, Imperial College – UK). This paper presents numerical results from finite volume modelling of full-scale test on medium density polyethylene gas pressurised pipes. The crack speed and pressure profile are prescribed in the analysis. Both steady-state and transient RCPs are considered, and the comparison between the two shown. The steady-state results are efficiently achieved employing a full multigrid acceleration technique, where sets of progressively finer grids are used in V-cycles. Also, the effect of inelastic behaviour of polyethylene on RCP results is demonstrated.     

Effect of loading rate on microstructural features of steel failure in crack propagation

A quantitative and qualitative fracture analysis has been carried out on 40Kh and St.3 steel specimens. The existence of a certain loading rate threshold has been established whose exceeding changes the regularities of the effect of the loading rate on the shape and parameters of the fracture microrelief. This corresponds to the speed dependence of dynamic crack resistance of steel.Translated from Problemy Prochnosti, No. 2, pp. 20–24, February, 1991.     

INTERFACIAL CRACK INITIATION UNDER QUASI-STATIC AND DYNAMIC LOADING CONDITIONS: AN EXPERIMENTAL STUDY

Abstract— Interfacial fracture parameters under quasi-static and dynamic loading are examined in a large elastic mismatch bimatenal system. A wide range of remote field loading ratios of shear and tension are considered. The crack tip fields are mapped using the optical method of coherent gradient sensing or CGS and fracture parameters are quantified. Distinctly different crack initiation responses are observed for positive and negative shear stresses acting on the interface. Also, low velocity impact loading experiments are conducted to study the influence of dynamic loading on crack initiation parameters. Dynamic interfacial crack tip fields are recorded using high speed photography and fracture parameters for dynamically loaded stationary cracks are obtained. Measurements suggest significant crack initiation toughness reduction under dynamic loading conditions.     

Bonding to aged surfaces: A thermally-aged epoxy

It is common experience that aged surfaces are often difficult to bond to. We report an examination of bonding to thermally-aged epoxy surfaces, using as the adhesive the same epoxy as that of the aged surface. The cured and postcured epoxy was aged at 200 ° C, with the ageing time varying from 2 to 8 h. The fracture energy of the bond line was measured by mode I cleavage under conditions of relatively slow crack growth. The bondline fracture energy was found to decrease logarithmically with ageing time. The fracture energies for bonds to surfaces aged for 2, 4, and 8 h at 200 ° C were 0.077, 0.059, and 0.050 kJ M^–2, respectively. These compare to 0.13 kJ M^–2 for a bond to an unaged surface and 0.21 kJ m^–2 for bulk fracture. Fracture surfaces resulting from both slow and rapid fracture were examined by optical and scanning electron microscopy. Fracture features different from those arising from bulk fracture were found. Areas with good adhesion occurred amidst fields of featureless fracture surface; the frequency and size of these areas decreased with increased ageing time. Evidence of plastic deformation was found, always occurring on the new side of the bond: ridges parallel with crack propagation at high crack speeds and subsurface undulations perpendicular to crack propagation at low speeds. The bond has the effect of channelling the crack along the bondline, but fracture does not always remain exactly at the interface. Fracture often occurred a relatively constant distance away from the interface, suggesting that the presence of the interface was felt for some distance.     

AN ANALYSIS OF FRICTIONAL EFFECTS ON CYLINDRICAL MODE III FATIGUE CRACK PROPAGATION SPECIMENS

Abstract— A model predicting the magnitude of frictional effects from fracture surface roughness on mode III fatigue crack growth is presened. Analysis of published data indicates that fracture surface roughness of the order of micrometers or less is enough to account for mode III fatigue crack growth retardation observation for increasing crack lengths for growth at constant Δ K . The model suggests that high strength materials will exhibit a greater resistance to shear crack growth than low strength materials. It also suggests that the resistance to shear crack growth will be more prominent at low nominal applied shear stress. The results of the analysis suggest that the concept of similitude does apply to mode III fatigue crack growth when the effects of friction on the stress intensity factor are included.     

Crack resistance behavior of particulate reinforced composites at various test speeds and temperatures

In this study, the fracture behavior and characteristics of particulate-reinforced composite materials were evaluated by performing wedge splitting tests. The crack resistance of the materials was evaluated using the crack tip opening displacement and crack tip opening angle. The composites were tested under various temperatures and test speeds. The digital image correlation method was used to analyze the strain field at the crack tip. The fracture surface under test conditions was observed using a scanning electron microscope. The test results showed that the fracture energy increased with decreasing temperature, and the crack resistance increased with increasing test speed. The crack tip opening angle is divided into an unstable region and stable region. The critical crack tip opening angle can be defined as the fracture mechanics parameter measured in a stable region. The surface strain fields obtained by digital image correlation method are distributed in the range from 1.5 % to 4.5 % at the initiation of the crack. A crack grows with dewetting phenomenon at the temperature range from 60 °C to −40 °C, and the crack propagates with fracture of ammonium perchlorate oxidizer particles at the glass transition temperature of −70 °C.     

Dynamic interaction of a propagating crack with a hole boundary

Summary The optical method of caustics was used along with high speed photography to study crack propagation and crack-hole interaction in plane PMMA specimens containing a transverse edge crack and a hole lying eccentrically to its axis. The specimens were fractured under different dynamic loads.Crack-hole interaction is characterized (for a limiting vertical distance of the crack axis from the center of the hole) by a process of attraction — repulsion of the crack towards the hole, interrupted by a momentary crack-arrest at the hole boundary. Increased values of crack propagation velocity and of the stress intensity factor at the tip of the propagating crack are detected during crack-hole interaction.With 7 Figures     

Rate and temperature effects on crack blunting mechanisms in pure and modified epoxies

The failure mechanisms of several epoxy polymers (including pure, rubber- and particulatemodified, as well as rubber/particulate hybrid epoxies) were investigated over a wide range of strain rates (10^–6 to 10² sec^–1) and temperatures (–80 to 60° C). A substantial variation in fracture toughness, G_Ic, with rate was observed at both very high and very low strain rates. Under impact testing conditions, G_Ic for both pure and rubber-modified epoxies displayed peaks at about 23 and –80° C which appeared to correlate with the corresponding size of the crack tip plastic zone. In order to explain these rate and temperature-dependent G_Ic results, two separate crack blunting mechanisms were proposed: thermal blunting due to crack tip adiabatic heating and plastic blunting associated with shear yield/flow processes. Thermal blunting was found to occur in the pure- and rubber-modified epoxies under all impact testing conditions and temperatures above 0° C. For temperatures below –20° C under impact conditions, the fracture toughness is dependent on viscoelastic loss processes and not thermal blunting. Plastic blunting was predominant at very slow strain rates less than 10^–2 sec^–1 for the pure- and rubber-modified epoxies and at impact strain rates for the fibre and hybrid epoxies. Microstructural studies of fracture surfaces provided some essential support for the two proposed crack blunting mechanisms.