Fracture mechanics parameters for polystyrene under high speed impact

A series of commercial polystyrenes was tested using an instrumented impact tester to determine the fracture toughness K_c and critical strain energy release rate G_c. Over the range of M_w, 201,000 to 336,000, K_c increased from 1.38 MN/m^3/2 to 1.76 MN/m^3/2and G_c from 0.92 kJ/m² to 1.60 kJ/m². A linear correlation for K_c and G_c was seen with melt index, and an inverse relationship was obtained against molecular weight. Examination of the fracture surfaces revealed the presence of crack growth bands corresponding to the crack tip plastic zone size. It is suggested that these bands are the consequence of variations in crack growth along crazes that form in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances. The spacing of these bands corresponds to the craze length formed in the plastic zone, and the band spacing increases with molecular weight.     

Effect of adhesion on the fracture toughness of calcium carbonate–filled polypropylene

The effect of adhesion on the strain energy release rate (G_c) and Charpy notched impact strength (NIS) of calcium carbonate (CaCO₃)-filled polypropylene (PP) at room temperature is investigated over a wide interval of particulate filler volume fractions. The concentration dependence of G_c and NIS are discussed in terms of competition between the effects of increasing stiffness, decreasing effective matrix cross section, and the transition from a plane strain to a plane stress mode of failure. In all cases the plane stress and plane strain limits of the critical strain energy release rate for initiation of cracks were not affected by the presence of the filler and are the same as those for neat matrix. In the case of no adhesion between components, the size of the crack tip plastic zone increases with increasing filler volume fraction (v_f) because of the reduction of the material yield strength. In the region 0 < v_f < 0.12, there is a mixed mode of failure, and the measured value of G_c for crack initiation increases steadily as the sample cross section approaches a fully plane stress state. The reduction in yield strength also results in the increase in G_c for crack propagation as reflected by an increase in NIS. Above v_f= 0.12, the specimen cross section is in a fully plane stress state, and further increase in filler volume fraction (decrease in matrix effective cross section) has the net effect of reducing both G_c and NIS. In the case of “perfect” adhesion, the yield strength increases only slightly with v_f. In the region 0 < yr < 0.05 there is also a mixed mode of failure, but the increase in G_c is much less than that for the no-adhesion case since the size of the plastic zone in front of the crack is much smaller. Above v_f= 0.05, the combined effects of increasing stiffness, reduction of the size of the plastic zone, and decreasing matrix cross section dominate the behavior, causing a steady reduction in both G_c and NIS. Good agreement was found between experimental data and calculations based on fracture mechanics principles.     

Numerical and experimental evaluation of the Mode III interlaminar fracture toughness of composite materials

The Crack Rail Shear (CRS) specimen is a proposed test method to characterize the interlaminar Mode III critical strain energy release rate (G_IIIc) of continuous fiber-reinforced composite materials. The specimen utilizes the two rail shear test fixture and contains embedded Kapton film between designated plies to provide a starter crack for subsequent fracture testing. Analytical expressions for specimen compliance and G_III are based upon Strength of Materials (SM) principles. The model identifies important material and geometric parameters and provides a simple data reduction scheme. A quasi-three-dimensional, linear elastic finite element stress analysis verifies the purity of the Mode III fracture state and identifies admissible crack lengths to be used in the experimental study. A fully three-dimensional linear elastic finite element analysis of the CRS is employed to investigate the influence of edge effects on the fracture state for the finite length sample. Results based upon a uniform crack extension indicate a small region of mixed mode behavior at traction free edges which decay to a pure Model III fracture state in the interior of the sample. Furthermore, the G_III distribution along the crack front decreases at the free edges from a maximum plateau region in the interior. The three-dimensional analysis allows edge effects to be minimized by selecting appropriate specimen lengths. Compliance and strain energy release rates are in good agreement with the SM model. An experimental program was performed to measure G_IIIc of two graphite epoxy systems. G_IIIc results for AS4/3501-6 were found to be 1.6 times the Mode II fracture toughness, while IM7/8551-7 exhibited equivalent Mode II and Mode III fracture toughnesses. Mode III fracture surfaces revealed microstructural deformations characteristic of Mode II fracture.     

Numerical simulation of the ENF test for the mode-II fracture characterization of bonded joints

In this work, the End Notched Flexure (ENF) test is analyzed in order to obtain the critical strain energy release rate in mode-II fracture of bonded joints. A cohesive model based on specially developed interface elements, including a linear softening damage process, is employed. The adequacy of the experimental ENF test is evaluated by numerical simulation. The objective is to compare the critical strain energy release rate in mode-II (G _{II c} ) obtained by different data reduction schemes with the real value which is an inputted parameter in the cohesive model. The effect of the Fracture Process Zone (FPZ) ahead of the crack tip is evaluated. A crack equivalent concept is proposed in order to account for the energy dissipated in the FPZ. A data reduction scheme avoiding the need to measure crack length is proposed. A good agreement with the inputted value of G _{II c} was obtained.     

Temperature effect on impact fracture toughness and fracture mechanism of phenolphthalein poly(ether ketone)

Phenolphthalein poly(ether ketone) (PEK-C) was tested using an instrumented impact tester to determine the temperature effect on the fracture toughness K_c and critical strain energy release rate G_c. Two different mechanisms, namely the relaxation processes and thermal blunting of the crack tip were used to explain the temperature effect on the fracture toughness. Examination of the fracture surfaces revealed the presence of crack growth bands. It is suggested that these bands are the consequence of variations in crack growth along crazes that are formed in the crack tip stress field. As the crack propagates, the stress is relaxed locally, decreasing the growth rate allowing a new bundle of crazes to nucleate along which the crack advances.     

The Fracture Toughness of Adhesive-Bonded Joints

Fracture mechanics is related to adhesion theory and the testing of adhesive-bonded joints in the lap-shear configuration. The complexity of the stress field necessitates the strain energy release rate approach, which is followed to derive the relation for a lap-shear sample: G_c = P_c²/4b (dC/da). G_c is the fracture toughness (critical strain energy release rate), P_c is the breaking or crack instability load, a and b are crack lengths and widths, respectively, and C is the sample compliance for the Tap-shear sample with a crack of these dimensions at each loading edge. It was found that G_c ranged from 1.18 to 1.42 with an average value of 1.34 in.-lb./in.² for epoxy bonded aluminum strips (EPON 934 and Alcald 2024-T3). Evidence, in the form of photoelastic stress patterns, suggesting that crack extension occurs in the opening mode in lap-shear samples is presented and discussed.     

Fracture and impact properties of polycarbonates and MBS elastomer-modified polycarbonates

Mechanical properties of polycarbonates (PCs) and elastomer-modified polycarbonates with various molecular weights (MW) are investigated. Higher MW PCs show slightly lower density, yield stress, and modulus. The ductile–brittle transition temperature (DBTT) of the notched impact strength decreases with the increase of PC MW and with the increase of elastomer content. The elastomer-modified PC has higher impact strength than does the unmodified counterpart if the failure is in the brittle mode, but has lower impact strength if the failure is in the ductile mode. The critical strain energy release rate (G_c) measured at ?30°C decreases with the decrease of PC MW. The extrapolated zero fracture energy was found at M_n = 6800 or MFR = 135. The G_c of the elastomer-modified PC (MFR = 15, 5% elastomer) is about twice that of thee unmodified one. The presence of elastomer in the PC matrix promotes the plane–strain localized shear yielding to greater extents and thus increases the impact strength and G_c in a typically brittle fracture. Two separate modes, localized and mass shear yielding, work simultaneously in the elastomer-toughening mechanism. The plane–strain localized shear yielding dominates the toughening mechanism at lower temperatures and brittle failure, while the plane–stress mass shear yielding dominates at higher temperatures and ductile failure. For the elastomer-modified PC (10% elastomer), the estimated extension ratio of the yielding zone of the fractured surface is 2 for the ductile failure and 5 for the brittle crack. A criterion for shifting from brittle to ductile failure based on precrack critical plastic-zone volume is proposed.     

The role of the polymer/metal interphase and its residual stresses in the critical strain energy release rate (Gc) determined using a three-point flexure test

The critical strain energy release rate (G _c), the residual stresses (σ), Young's modulus (E), and the practical adhesion, characterized by ultimate parameters (F_max or d_max), of organic layers made of DGEBA epoxy monomer and IPDA diamine hardener were determined. The prepolymer (DGEBA-IPDA) was deposited both as thick coatings and as a mechanical stiffener onto degreased aluminum alloy (5754) or chemically etched titanium alloy (Ti-6Al-4V). During the three-point flexure test used as a practical adhesion test [this test is also called the double cantilever adhesion test (DCAT)], the failure may be regarded as a special case of crack growth. To understand the real gradient properties of the interphase, substrate, and bulk polymer properties, a three-layer model was developed for quantitative determination of the critical strain energy release rate (G_c). The particular characteristic of this model was to consider the residual stresses developed within the entire three-layered system, leading to an intrinsic parameter representing the practical adhesion between a polymer and a metallic substrate. Moreover, to determine the residual stresses generated in such three-layer systems, the gradient of interphase mechanical properties was considered. The maxima of residual stress intensities are found at the interphase/substrate interface, leading to an adhesional (interfacial) failure that is experimentally observed. The determination of the critical strain energy release rate by the three-point flexure test (DCAT) shows that residual stresses cannot be neglected. A comparison between the results obtained from the three-point flexure test (DCAT) and those obtained by the tapered double cantilever beam (TDCB) test is presented.     

On the significance of the standardized notched impact strength for materials selection and design

Experimental data on the standard Charpy notched impact strength (CNIS) for a large sampling of particulate-filled and rubber-modified polypropylenes were analyzed. To determine the significance of the CNIS for material selection and design, CNIS data were compared with fracture toughness measurements expressed as the critical strain energy release rate G′_c, measured under impact loading. A scale factor representing the state of stress at the crack tip was calculated, assuming small scale yielding, Class I linear elastic fracture mechanics (LEFM). Based on the data, three principal groups of materials were identified. In the smallest of the three, CNIS and G′_c measurements showed the same functional dependence on the material variables studied and were characterized by a scale factor independent of the composition. In these cases, one can justify comparisons of toughness of different compositions using single values of the CNIS, since the materials are probably being compared in equivalent states of stress. In a second group, CNIS and G′_c also show the same functional dependence on material variables, but exhibit large variations in the scale factor with composition. One should not compare the toughness of different materials from this group based on single values of CNIS, since it is likely that the comparisons would not be made relative to equivalent states of stress. In these cases, only measurements of G′_c can separate the effect of specimen geometry from those of the intrinsic properties of the material. The majority of materials studied fell into a third group, in which the CNIS and G′_c exhibited substantially different functional dependencies on the material properties, and the scale factors depended also on composition. In these latter cases, a comparison of CNIS values for different compositions is not a reliable indication of the relative toughness and is of little value as a parameter for material selection and design.     

Impact behavior of a short glass fiber reinforced thermoplastic polyurethane

The temperature dependence of critical strain energy release rate (G_c′) and standardized Charpy notched impact strength (CNIS) were measured for a thermoplastic polyurethane (TPUR) reinforced with 30 wt% of short glass fibers (SGF) over a temperature interval ranging from −150°C 23°C (RT) at two strain rates, 70 and 150 s⁻¹, respectively. Fractographic observation of fracture planes was used to qualitatively assess the fracture modes and mechanisms. Adhesion between the reinforcement and the matrix was excellent and the integrity of the fiber‐matrix interfacial contact was relatively insensitive to exposure to hydrolysis during the immersion in boiling water for 100 hours. At temperatures above −30°C, there was a large extent of plastic deformation in the vicinity of crack planes while at temperatures below −50°C, the extent of plastic deformation was substantially reduced. This resulted in a change in the major energy dissipation mechanism and led to a decrease of both CNIS and G_c′ values for SGF/TPUR composites. It was suggested that the plastic deformation of TPUR matrix in the immediate vicinity of glass fibers was the primary source of energy dissipation at temperatures above −30°C, while the friction and fiber pull‐out was the main dissipative process below −50°C. Over the whole temperature interval investigated, greater G_c′ values were obtained at higher strain rate of 150 s⁻¹, without any significant change in the fractographic patterns observed on the fracture planes. The CNIS/G_c′ ratio, used to assess suitability of CNIS for comparison of materials, changed with temperature substantially suggesting that the functional dependences of CNIS and G_c′ on temperature differ substantially. Hence, CNIS data do not provide a reliable base for material selection and for design purposes in this case.     

Fracture toughness and mechanical properties of poly(n-pentyl-n-alkylsilanes)

The mechanical properties and fracture toughness of thin films of a series of poly(n-pentyl-n-alkylsilanes) were investigated. Poly(n-butyl-n-pentylsilane) is the strongest of these polymers with an elastic modulus of 2.96 × 10⁸ Pa and a fracture strain of 85% at 25°C. The hexagonal mesophases of these polymers generally show elastic moduli on the order of 10⁷ Pa and are often quite extensible. A J-integral analysis of the ductile tearing of thin films of poly(n-butyl-n-pentylsilane) and poly(n-propyl-n-pentylsilane) using an Instron tensile testing machine and specimens in the single edge notch (SEN) geometry yielded plane stress J_1c (critical value of J for fracture initiation) of 1745 J/m² and 205 J/m², respectively. Both values are significantly higher than the plane stress G_1c (critical energy release rate) value of 109 J/m² obtained for poly(di-n-hexylsilane) with a residual stress analysis using the same apparatus and testing procedure.     

The impact behavior of ABS over a range of temperatures

Charpy type tests have been conducted on a typical grade of aerylonitrile-butadiene-styrene (ABS) over the temperature range +60 to ?80°C. At the higher temperatures, the fractures were fully ductile and have been explained in terms of a constant energy density necessary to produce craze-whitened material. Below ?40°C, the results were analyzed using a linear elastic fracture mechanics approach and values of G_c, the critical strain energy release rate, were obtained. The intermediate temperatures produced partially-ductile behavior and these data were also analyzed to yield effective values of G_c.     

Evaluation of methods of determining fracture parameters for a glassy polymer: Poly(methyl methacrylate)

Fracture criteria for the brittle fracture of a glassy thermoplastic, poly(methyl methacrylate), have been evaluated using three test piece geometries; the double cantilever beam (DCB), three-point bend (TPB), and compact tension (CT). For the DCB good agreement is obtained with published estimates of the fracture parameters using either a compliance calibration calculation for the critical energy release rate, G_1c, or a polynomial function for the critical stress intensity factor, K_1c. Anamolously high values of G_1c or K_1c were obtained using the TPB test piece. These high values of K_1c may be partially due to the difficulty of “sharpening” the crack, but there is a test piece size effect which also contributes to the over estimation of K_1c. For the CT test piece use of either a new compliance calibration for the determination of G_1c or a standard polynomial function for K_1c, good agreement was obtained with our own DCB and other published data. The range of applicability of the CT test geometry is discussed critically, and with some reservations it is considered suitable for the evaluation of either G_1c or K_1c.     

Fracture toughness of adhesive joints. II. Temperature and rate dependencies of mode I fracture toughness and adhesive tensile strength

It has been known that adhesive strength shows temperature and rate dependencies reflecting visoelastic properties of an adhesive. Similarly, a critical strain energy release rate is expected to show temperature and time dependencies deformation and fracture of the adhesive occurs at the time of measurement of the critical strain energy release rate, which is a kind of fracture mechanical parameter for adhesive joints. The term “critical strain energy release rate” has usually been called “fracture toughness.” In this study, the critical strain energy release rate (G_IC) of the opening mode was called mode I fracture toughness. G_IC was measured over a wide range of temperatures and rates, and then a master curve was obtained by applying the temperature–rate superposition principle to the obtained data. Also, on the relation between G_IC and adhesive tensile strength is discussed. © 1995 John Wiley & Sons, Inc.     

Fracture toughness of filled polypropylene copolymer systems

The impact strength to stiffness balance of a toughened polypropylene copolymer was modified through the addition of mineral fillers. The stiffness was improved over the base resin value for all formulations. However, the impact strength exhibited complex behavior. The fracture toughness G_c calculated using the linear elastic fracture mechanics theory was indicative of the materials resistance to crack propagation. The G_c values were modified significantly with the addition of fillers and for some formulations was greater than the base resin value. The LEFM analysis indicates that this is due to an increase in the damage zone size r_p where the energy absorbing mechanisms are concentrated. However, the specific energy absorbed per unit volume decreased with the addition of fillers. The total energy to fracture measured using unnotched samples was indicative of crack initiation and crack propagation energies. This upper bound value decreased for all formulations indicating a reduction in the crack initiation resistance, in the presence of stress concentrating heterogeneities in the filled systems.     

Impact and dynamic fracture resistance of crystalline thermoplastics: Prediction from bulk properties

The behavior of tough, crystalline thermoplastics in notched impact tests leads to the definition of crack initiation resistance and propagation resistance as two distinct properties, G_c and G_D. It is shown here that a single criterion—adiabatic thermal failure of a crack-tip cohesive zone—can be applied to predict both. Dynamic fracture resistance G_D emerges as a geometry independent, though crack speed and temperature dependent, material property, whose minimum value G_D,min depends only on temperature and bulk physical properties. G_D,_min can be measured using a simple pressurized-tube test. Crack initiation resistance G_c, however, is inherently influenced by geometry and impact speed, although its lower bound is also G_D,min. Craze extension and failure of a notched impact specimen, and hence G_c, can be predicted for a specific temperature, given bulk thermal property data and a dynamic stress/strain curve measured by impact bending of an unnotched beam. For materials that comply with the model, sharp-notched Charpy type impact tests will not arrive at a unique G_c value, while Izod type tests, for which a revised compliance calibration is presented, may fail to establish any G_c value at all.     

Crack tip damage analysis in fatigue fracture of epoxy resin

The application of the crack layer theory to fatigue crack propagation (FCP) in epoxy is discussed. A crack tip damage evolution coefficient μ is introduced to assess the extent of damage as a fraction of the damage associated with critical crack propagation. The results can be expressed in the form where dl/dN is the rate of FCP, G₁ is the energy release rate whose critical value is G_1c, and β is a phenomenological constant. Although no damage was detected from microscopic analyses, μ increases fivefold during stable crack propagation. Fractal analysis of fracture surface profiles provides a quantitative measure of the roughness associated with crack advance. The fractural measure d is found to evolve in a similar fashion as μ, suggesting the applicability of d to quantify crack tip damage evolution.     

Elucidating the Crack Resistance of Alkali‐Activated Slag Mortars Using Coupled Fracture Tests and Image Correlation

The resistance of alkali silicate‐activated slag mortars to crack propagation is explored. With increasing SiO₂‐to‐alkali oxide ratio (M_s) of the activating solution (between 1.0 and 2.0), the flexural strengths, fracture energies, and the strain energy release rates (crack resistance, G_R) are noted to increase. The G_R values, especially of the systems with M_s of 1.5 and 2.0, are higher than that of ordinary portland cement (OPC) mortar. In contrast, the fracture process zone (FPZ) was observed to be smaller for the alkali‐activated slag mortars, with higher localized strains. Similarly, the FPZs also shrink with increasing M_s. These responses are related to the differences in the reaction products in these systems. The fundamental differences in the fracture response of these binder systems are elucidated through tracking the FPZ development. The crack extension‐crack tip opening displacement relations and its relationship with the inelastic strain energy release rates are also used to bring out the differences between the binder systems.