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.     

Temperature effects in the fracture of PMMA

Experiments are described in which the fracture toughness,K _c, of PMMA has been determined in the temperature range –190 to + 80° C and over the crack speed range of 10^–2 to 10² mm sec^–1. Single edge notch tension was used for instability measurements but the other data were obtained using the double torsion method. In the range –80 to + 80°C the variations inK _c may be described in terms of modulus changes and a constant crack opening displacement criterion. Crack instabilities are correlated with isothermal-adiabatic transitions at the crack tip. Below –80° C there is an inverted rate dependence associated with thermal effects during post-instability crack propagation.     

Effects of thickness and environmental temperature on fracture behaviour of polyetherimide (PEI)

The fracture behaviour of a polyetherimide (PEI) thermoplastic polymer was studied using compact tension (CT) specimens with a special emphasis on effects of specimen thickness and testing temperatures on the plane strain fracture toughness. The results show that the valid fracture toughness of the critical stress intensity factor, K _IC, and strain energy release rate, G _IC, is independent of the specimen thickness when it is larger than 5 mm at ambient temperature. On the other hand, the fracture toughness is relatively sensitive to testing temperatures. The K _IC value remains almost constant, 3.5 MPa in a temperature range from 25 to 130°C, but the G _IC value slightly increases due to the decrease in Young's modulus and yield stress with increasing temperature. The temperature dependence of the fracture toughness, G _IC, was explained in terms of a plastic deformation zone around the crack tip and fracture surface morphology. It was identified that the larger plastic zone and extensive plastic deformation in the crack initiation region were associated with the enhanced G _IC at elevated temperatures.     

Influence of mixed mode I/III loading on fracture toughness of mild steel at various strain rates

Abstract

The effect of loading angle &phis; on the fracture toughness of mild steel at various strain rates has been studied. The fracture toughness was found to decrease with increasing loading angle (or increasing mode III component) at strain rates 10^-5 to 10⁰ s^-1 where ductile fracture was observed. Under impact conditions (strain rate 10² s^-1), fracture was by cleavage and the fracture toughness was found to increase with increasing loading angle. The results showed that the mixed mode fracture behaviour of mild steel changed from Class C in the strain rate range 10^-5 to 10⁰ s^-1 to a combination of Class A and B under impact conditions. In the strain rate range 10^-5 to 10^-2 s^-1, the fracture toughness behaviour with increasing strain rate was found to be similar for the three loading angles studied, namely &phis;= 0, &phis;= 30 and &phis;= 45°. At the strain rates 10^-2 to 10² s^-1, fracture toughness at &phis;= 0° decreased sharply, while for loading angles &phis;= 30° and &phis;= 45°, the fracture toughness increased with strain rate. The increase in mixed mode fracture toughness with strain rate in this strain rate regime has been attributed to the inertial effects which are known to reduce the T stress ahead of the crack.     

Fracture behavior dependence on load-bearing capacity of filler in nano- and microcomposites of polypropylene containing calcium carbonate

The fracture toughness and deformation mechanism of PP/CaCO₃ (15 wt.%) composites were studied and related to load-bearing capacity of the particles. To alter the load-bearing capacity of the particles, different particle sizes (0.07–7 μm) with or without stearic acid coating were incorporated. The fracture toughness of the composites was determined using J-Integral method and the deformation mechanism was studied by transmission optical microscopy of the crack tip damage zone. It was observed that the load-bearing capacity of the particles decreased by reduction of particle size and application of coating. A linear relationship between normalized fracture toughness and inverse of load-bearing capacity of particles was found. The crack tip damage zone in composites, which consists in massive crazing, further grows by reduction in load-bearing capacity.     

Review Mechanical properties of ice and snow

The mechanical properties of ice and snow are reviewed. The tensile strength of ice varies from 0.7–3.1 MPa and the compressive strength varies from 5–25 MPa over the temperature range –10°C to –20°C. The ice compressive strength increases with decreasing temperature and increasing strain rate, but ice tensile strength is relatively insensitive to these variables. The tensile strength of ice decreases with increasing ice grain size. The strength of ice decreases with increasing volume, and the estimated Weibull modulus is 5. The fracture toughness of ice is in the range of 50–150 kPa m^1/2 and the fracture-initiating flaw size is similar to the grain size. Ice-soil composite mixtures are both stronger and tougher than ice alone. Snow is a open cellular form of ice. Both the strength and fracture toughness of snow are substantially lower than those of ice. Fracture-initiating flaw sizes in snow appear to correlate to the snow cell size.     

Flaw growth in a polycrystalline lithium-aluminium-silicate glass ceramic

The growth of indentation-produced controlled flaws in a polycrystalline lithium-aluminium-silicate glass ceramic has been studied, over a wide range of temperatures and strain rates. Significant scatter in the fracture stress at elevated temperatures suggests that the extent of slow crack growth is highly sensitive to microstructural details. The initial flaw shape is important inK _IC determination. Up to 1000° C the fracture toughness,K _IC, is essentially strain-rate insensitive. The value ofK _IC decreases with temperature beyond 850° C. Intergranular cavity formation is suggested as the reason. Crack blunting by diffusive crack healing probably occurs at high temperatures. Also, intergranular slow crack growth occurs essentially under Mode I loading.     

Constraint Loss under Dynamic Loading in Rate Independent Plastic Solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J ₂ flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J–Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K _dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K _dc for .     

Fracture toughness of sea ice

Linear elastic fracture mechanics, which has been applied to fragile substances and successfully used for studying the brittle fracture of metallic materials, was utilized to gain an understanding of the fracture phenomena of sea ice.The present paper reports the first results of investigations into the fracture-toughness value of sea ice, which was analyzed experimentally as a function of strain rate on the basis of the stress-intensity-factor concept.The fracture toughness, K_IC, of sea ice, which was measured by an in-situ three-point bending test on notched specimens, shows almost constant value if the strain rate is less then 10^?3 s^?1 and decreases with increasing strain rate if the strain rate exceeds 10^?3 s^?1. K_IC data show considerably less scatter than existing data such as the compressive, tensile and flexural strengths.It was confirmed in the present study that the linear elastic-fracture-mechanics concept is effective for analyzing the fracture phenomena of sea ice. Moreover, the K_IC value was shown to be closely related to sea-ice structures (e.g. the size of crack-like flaws such as brine cells).It is also suggested that the fracture-toughness test might prove to be a standard testing method to obtain the sea-ice strength, since once K_1C and crack-like flaw sizes are determined, the less-scattered critical-fracture stress can be calculated.     

Fracture Parameters for Natural Rubber Under Dynamic Loading

Abstract: An experimental study was conducted to evaluate the tear energy of unfilled and 25 phr carbon black‐filled natural rubber with varying loading rates. The variation of the tear energy with far‐field sample strain rate between 0.01 to 10 s^?1 was found to be different from tensile strip and pure shear specimens. Above a sample strain rate of 10 s^?1, the tear energy calculated from either specimen was comparable. The differences in the tear energy derived from the tensile strip and pure shear specimens were attributed to differences in the local crack tip stress state and strengthening of the material due to strain‐induced crystallisation. Both of these factors resulted in crack speeds 3–4 times higher in the pure shear specimen as compared to the tensile strip specimen. Finite element analysis (FEA) indicated that fracture would initiate at the crack tip either when the strain energy density approached the material toughness or when the maximum principal stress and strain approached the material tensile strength and fracture strain, respectively. It was concluded that these parameters would be better than the tear energy in predicting fracture of natural rubber under dynamic loading.     

Mechanical properties of vanadium beryllide,VBe12

The mechanical properties of VBe₁₂, both at room and elevated temperatures (up to 1200°C), have been measured. Room-temperature properties, including Young's modulus, flexural strength, and fracture toughness are reported. The material behaved elastically at room temperature but became plastic at temperatures above 1000°C. Creep properties of VBe₁₂ were also studied in temperature ranges from 1000–1200°C and applied stress ranges from 33–58 MPa. At low strain rates (approximately < 10^–5s^–1), the stress exponent was about 4, suggesting deformation was controlled by dislocation climb. Microstructural examination indicated that fracture was initiated from grain boundaries subjected to tensile stresses. The creep behaviour of VBe₁₂ is briefly compared with that of other intermetallics.     

Size effect on the fracture toughness of metallic foil

The size effects on fracture behavior of Cu foil are investigated by a new optical technique, the digital speckle correlation method (DSCM). Displacement and strain fields around a crack tip are analyzed for different thicknesses of Cu foil. Then, the J integral and fracture toughness J _C are evaluated directly from the strain fields around the crack tip. The fracture toughness J _C is obtained as a function of foil thickness. The results indicate that J _C indeed depends on foil thickness within a certain range of thickness (the thickness varies from 20 micron to 1 millimeter in this work).     

The influence of weld strength mismatch on crack-tip constraint in single edge notch bend specimens

Previous work by Dodds and Anderson provides a framework to quantify finite size and crack depth effects on cleavage fracture toughness when failure occurs at deformation levels where J no longer uniquely describes the state of stresses and strains in the vicinity of the crack tip. Size effects on cleavage fracture are quantified by defining a value termed J _SSY: the J to which an infinite body must be loaded to achieve the same likelihood of cleavage fracture as in a finite body. In weld metal fracture toughness testing, mismatch between weld metal and baseplate strength can alter deformation patterns, which complicate size and crack depth effects on cleavage fracture toughness. This study demonstrates that there is virtually no effect of ±20 percent mismatch on J _SSYif the distance from the crack tip to the weld/plate interface (L _min) exceeds 5 mm. At higher levels of overmatch (50 to 100%), it is no longer possible to parameterize the departure of J _SSYfor a weldment from that for a homogeneous SE(B) based on L _min alone. Weld geometry significantly influences the accuracy with which J _SSYfor a welded SE(B) can be approximated by J _SSYfor a homogeneous specimen at these extreme overmatch levels.     

Low-temperature fracture toughness study of Fe-7Al-27Mn-C alloys

This research studied the fracture toughness of the Fe-7Al-27Mn alloys with increasing carbon contents: 0.5% C, Fl alloy: 0.7% C, F2 alloy (with 4.0% Cr); and 1.0% C, F3 alloy. Fracture toughness experiments were conducted at temperatures of 25, – 50, – 100 and – 150 °C. It was found that plane-stress,K _C, values as measured by the R-curve method, decreased as the temperature dropped. F1 alloy possessed the highestK _C value at all temperatures among the three alloys. TheK _C values of the F2 and F3 alloys were similar at ambient temperatures, but F3 maintained the toughness property and ductility better at sub-zero temperatures. Quantitatively,K _IC values of the F2 alloy at – 150 °C were ca, 60% less than at 25 °C, but F1 and F3 alloys dropped by only ca. 30%. Using a compact-tension specimen, 20.0 mm thick, at –150°C only alloy F2 satisfied the requirement of plane-strain fracture toughness with aK _C value of 106 MPa m^1/2. The existence of Cr (4.0%) and the formation of a ferrite phase in an austenite matrix was responsible for the low toughness value observed.     

Recrystallization-etch approach to study the plastic energy absorbtion at crack initiation and extension of pressure-vessel steel A533B-1

To evaluate the elastic-plastic fracture toughness parameter of nuclear pressure-vessel steel A533B-1, a newly developed technique (the recrystallization-etch technique) for plastic strain measurement was applied to different sizes of compact tension specimens with a crack length/specimen width of 0.6–0.5 that were tested to generate resistance curves for stable crack extensions. By means of the recrystallization-etch technique, the plastic energy dissipation or work done within an intense strain region at the crack tip during crack initiation and extension was measured experimentally. Furthermore, the thickness effects on this crack tip energy dissipation rate were examined in comparison with other fracture-parameter J integrals. Thickness effects on critical energy dissipation and energy dissipation rate during crack extension were obtained and the energy dissipation rate dW _p/da in the mid-section shows a constant value irrespective of specimen geometry and size, which can be used as a fracture parameter or crack resistance property.     

Constraint-modified J−R curves and its application to ductile crack growth

The concept of J-controlled crack growth is extended to J–A ₂ controlled crack growth using J as the loading level and A ₂ as the constraint parameter. It is shown that during crack extension, the parameter A ₂ is an appropriate constraint parameter due to its independence of applied loads under fully plastic conditions or large-scale yielding. A wide range of constraint level is considered using five different types of specimen geometry and loading configuration; namely, compact tension (CT), three-point bend (TPB), single edge-notched tension (SENT), double edge-notched tension (DENT) and centre-cracked panel (CCP). The upper shelf initiation toughness J _IC, tearing resistance T _R and J–R curves tested by Joyce and Link (1995) for A533B steels using the first four specimens are analysed. Through finite element analysis at the applied load of J _IC, the values of A ₂ for all specimens are determined. The framework and construction of constraint-modified J–R curves using A ₂ as the constraint parameter are developed and demonstrated. A procedure of transferring the J–R curves determined from standard ASTM procedure to non-standard specimens or practical cracked structures is outlined. Based on the test data, the constraint-modified J–R curves are presented for the test material of A533B steel. Comparison shows the experimental J–R curves can be reproduced or predicted accurately by the constraint-modified J–R curves for all specimens tested. Finally, the variation of J–R curves with the size of test specimens is produced. The results show that larger specimens tend to have lower crack growth resistance curves.     

Crack velocity dependence of longitudinal fracture in bone

An evaluation of the fracture characteristics of bovine tibia compact tension specimens associated with controlled crack propagation in the longitudinal direction has been made. The fracture mechanics parameters of critical strain energy release rate (G _c) and critical stress intensity factor (K _c) were determined for a range of crack velocities. A comparative fracture energy (W) was also evaluated from the area under the load-deflection curve. It was found that an increase in the average crack velocity from 1.75 to 23.6×10^–5 m sec^–1 produced increases in G _c (from 1736 to 2796 J m^–2), K _c (from 4.46 to 5.38 MN m^–3/2) and W. At crack velocities >23.6×10^–5 m sec^–1, W decreased appreciably. Microstructural observations indicated that, for crack velocities <23.6 m sec^–1, relatively rough fracture surfaces were produced by the passage of the crack around intersecting osteons (or lamellae), together with some osteon pull-out. In contrast, at a higher crack velocity, fracture was characterized by relatively smooth surfaces, as the crack moved indiscriminately through the microstructural constituents.     

Thermodynamical approach to the brittle fracture of dry plasters

The evolution of the fracture toughness, K _lc, and fracture energy, G _lc, of set plasters was determined on notched beams as a function of sample porosity, P, and characteristic size, W. Toughness was found to decrease with decreasing crack width. For set plasters of 57.7% porosity, the lowest toughness measured was K _lc=0.13 MPa m^1/2 for a crack width of 0.2 mm. For this crack width, fracture toughness and fracture energy linearly changed with porosity: K _lc=0.5 1–1.3 P) MPa m^1/2 and G _lc= 13.47 (1–1.12 P) Jm^–2. Dense plasters were more difficult to break than porous ones. The fracture energies were affected by the velocity of the fracture propagation, which induces damaging and multicracking of the material, so that the roughly calculated chemical surface energy of set plaster was too high. After correction it was estimated to be 0.4 J m ^–2. Finally, because toughness increased with increasing sample size, it was concluded that fracture toughness and energy were not intrinsic parameters of the material. On the other hand, for our sample porosities and sizes, the reduced rupture force, F _rupt W ^–0.65 is a constant and seems to be a characteristic parameter of the mechanical resistance of set plaster beams.     

A mechanical model to predict elastic-plastic fracture toughness in high strength materials

A mechanical model of crack initiation and propagation, which is based on the actual mechanism of ductile fracture in high strength materials, is proposed. Assuming that a crack initiates when the equivalent stress at a distance ρ from the crack tip reaches a critical value $\text{}\text{?}$gsf, an equation for predicting fracture toughness J_IC is obtained. From comparison between the predicted values and the experimental results, it is found that the distance ρ corresponds to the spacing of micro-inclusions. The temperature dependence of fracture toughness J_IC estimated according to the derived equation is given in an Arrhenius form of equation and is nearly consistent with the experimental results.     

Processing maps for hot-working of powder metallurgy 1100 Al-10 vol % SiC-particulate metal-matrix composite

The hot-working characteristics of the metal-matrix composite (MMC) Al-10 vol % SiC-particulate (SiC_p) powder metallurgy compacts in as-sintered and in hot-extruded conditions were studied using hot compression testing. On the basis of the stress-strain data as a function of temperature and strain rate, processing maps depicting the variation in the efficiency of power dissipation, given by = 2m/(m+1), where m is the strain rate sensitivity of flow stress, have been established and are interpreted on the basis of the dynamic materials model. The as-sintered MMC exhibited a domain of dynamic recrystallization (DRX) with a peak efficiency of about 30% at a temperature of about 500°C and a strain rate of 0.01 s^–1. At temperatures below 350°C and in the strain rate range 0.001–0.01 s^–1 the MMC exhibited dynamic recovery. The as-sintered MMC was extruded at 500°C using a ram speed of 3 mm s^–1 and an extrusion ratio of 101. A processing map was established on the extruded product, and this map showed that the DRX domain had shifted to lower temperature (450°C) and higher strain rate (1 s^–1). The optimum temperature and strain rate combination for powder metallurgy billet conditioning are 500°C and 0.01 s^–1, and the secondary metal-working on the extruded product may be done at a higher strain rate of 1 s^–1 and a lower temperature of 425°C.