Determination of fracture toughness and fracture energy of brittle materials under impact wedging

Abstract

539.375 1. Test Procedure. Modern fracture mechanics is characterized by an advanced mathematical apparatus and a high level of experimental facilities [1]. The available theoretical and experimental methods allow one to determine criterion parameters for various types of loading. Standard methods of determination of fracture toughness Klc in statics, Kid in dynamics, and the dynamic stress intensity factor (SIF) in crack growth KD or arrest Kla have been developed [2, 3].In high-speed loading for a characteristic loading time of (1-5) 9 10 -3 sec and smaller using standard loading schemes, difficulties arise which are due to dynamic effects.We used stress-wave loading of a specimeu by the Hopkinson split bar (HSB) method to determine the fracture toughness and fracture energy of brittle materials under high-speed loading.Hopkinson proposed to determine stresses in a shock-wave pulse propagating in a bar under explosive loading from the rebound velocity of a measuring bar which is butt-joined with a loading bar [4]. The fracture stresses of brittle materials under tension are considerably lower than those under compression, and a spall forms in bars under intense pulse loading. Khanukaev [5] determined critical spalling stresses in rocks (granite, marble, etc.) from the velocity of the part spalled from the bar, using the Hopkinson method.Ivanov [6] reported determination of fracture energy in spalling experiments using the integral energy criterion. Kol'skii improved the Hopkinson method. He proposed to measure the wave velocities of transmitted pulses and to compute stresses and strains in a specimen placed between two bars using measured parameters of incident, reflected, and transmitted pulses [7]. Later, the HSB method led to many applications in various types of uniaxial dynamic loading experiments, including determination of fracture toughness.Novikov [8] reported experiments on determination of the dynamic fracture toughness of hard alloys loaded by the HSB method. Specimens in the form of disks (tablets) with a through central cut loaded in the diametric direction were tested.An original procedure for determining the fracture toughness of steels and alloys was proposed by Kostin et al. [9]. A bar having a ringed cut with a sharp (fatigue) crack in the base of the cut is subjected to shock-wave loading. As a specimen, the part of the bar neighboring the cut is studied. According to the HSB method, the stresses and forces P in the section of the crack and also the strains 6 due to its opening are determined and a quasi-static P -6 diagram is constructed and analyzed by the standard method. The dynamic fracture toughness Kid and the fracture energy Gc are determined from the P -~ diagram. In the case of plastic materials, the calculation is performed using the J-integral.The growth rate of SIF iswhere r, is the characteristic time of increase in load from zero to a load that corresponds to a critical state. The attainable loading rate for steels is of the order of 10 6 (MPa 9 m 1/2) sec -1. This is app...

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

“…To study systematically the effect of loading rate, the striker was launched by a gas gun at speeds ranging from 2.0 to 5.0 m/s. Figure 2b shows the photograph of loading configurations and a NSCB specimen with random speckle patterns on the surface that was applied to ensure good contrast of the images for the calcu- (Atkinson et al 1982) K Id , K IId (Nakano et al 1994) One (Klepaczko et al 1984) K Id (Klepaczko et al 1984) Two-bar SHPB Coal K Id (Eremenko et al 1996) Granite SR K IC (Ouchterlony 1988) K Id (Costin 1981) Charpy impact machine (Mindess et al 1987) Concrete Peak load K Id (Zhao et al 1999) Pneumatichydraulic machine Granite K Id (Tang and Xu 1990) One-bar SHPB (Chen et al 2009) Granite K ID (Chen et al 2009) Granite…”

Time‐ and Temperature‐Dependent Fracture Mechanics of Polymers: General Aspects at Monotonic Quasi‐Static and Impact Loading Conditions

“…Arrhenius diagram from local maxima in toughnesstemperature or toughness-loading speed diagrams and tan d-temperature diagrams for PC, PMMA, PVC, PP, PTFE and PA 6; authors' own data and data from literature. [46,55,62,63,[65][66][67] loading speed can be set into superposition using the time/ temperature equivalent principle both for mode I [59,60] and mode II loading. [58] The relationship between the fracture toughness and the time established in this way qualitatively conforms to the time dependence of the imaginary part of the dynamic modulus of elasticity (loss modulus).…”

“…[64] for PMMA). [65][66][67] The above statement can be verified by investigations into the toughness values K I of PVC as functions of loading speed and temperature. [46] The local maximum of K I ¼ f(T) shifts by 23 K towards higher temperatures when increasing the fracture frequency f B from f B ¼ 11 Hz (quasi-static loading) to f B ¼ 800 Hz (impact-like loading) (compare Figure 6).…”