Critical stress energy release rate

Fig. 52. Critical stress intensity factor, Kj, and critical stress energy release rate, of solvent-modified, semi-porous, and macroporous epoxies prepared via kinetically controlled Cl PS with 1 wt % catalyst calculated from SENB tests...

More specific values of the fracture toughness are obtained by the application of the experimental procedures derived from the fracture mechanics theories. In the case of no plastic deformation in front of the crack tip, the LEFM is employed, obtaining the values of the stress critical intensity factor (fQ) or critical stress energy release rate (G,.). On the other hand, when there is plasticity in front of the crack tip, we must use the principles of the elastoplastic fracture mechanics in this sense, two experimental procedures are widely employed the J-integral analysis and the EWF. 

Step 2. After a contact time t, the material is fractured or fatigued and the mechanical properties determined. The measured properties will be a function of the test configuration, rate of testing, temperature, etc., and include the critical strain energy release rate Gic, the critical stress intensity factor K[c, the critical... 

Critical stress intensity factor Klc and critical strain energy release rate G1C quantify the stability of a polymer against the initiation and propagation of cracks. Stress intensity factor and energy release rate G, are not independent but they are related [76] by means of the appropriate modulus E. ... 

The term fracture toughness or toughness with a symbol, R or Gc, used throughout this chapter refers to the work dissipated in creating new fracture surfaces of a unit nominal cross-sectional area, or the critical potential energy release rate, of a composite specimen with a unit kJ/m. Fracture toughness is also often measured in terms of the critical stress intensity factor, with a unit MPay/m, based on linear elastic fracture mechanics (LEFM) principle. The various micro-failure mechanisms that make up the total specific work of fracture or fracture toughness are discussed in this section. 

Materials Young s Modulus (GPa) Ultimate Tensile Strength (MPa) Critical Stress Intensity Factor K c (MN m- /2) Critical Strain Energy Release Rate, G c (J m-2)... 

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

On comparing Eqs. (10.3) and (10.6), we see that the critical stress intensity factor, Kc, and the fracture energy, or critical strain energy release rate, Gc, are related to each other and to the breaking stress at the crack tip, as follows ... 

The fracture toughness, a term defined by Irwin (1956, 1960) to characterize brittleness, provides a measure of the conditions required for catastrophic crack propagation in a material (see Section 1.6). One fracture toughness parameter is the surface fracture energy y, defined as one-half G, the critical strain energy release rate above which catastrophic failure occurs. In turn G is related to another convenient toughness parameter, the critical stress intensity factor a measure of the stress field at the crack tip. For fracture of an isotropic material in a plane strain modet (Baer, 1964, p. 946) ... 

Mechanical property measurements quantify epoxy suitability for structural applications. Shear modulus, the critical strain energy release rate (G ) and the critical stress intensity factor (Kj,) are especially useful for this purpose. 

The crucial practical consequence of constraint at the crack tip (under the imposed plane-strain conditions) is that it inhibits crack tip plastic deformation, and consequently reduces the critical strain energy release rate to a value below G. Similarly, the critical stress intensity factor falls below K. ... 

Charpy impact testing can also be used to determine critical strain energy release rates, G/, and to estimate the values of fracture toughness in states of plane strain and plane stress, and G c, respectively (49,89). Hence, experimental data can be obtained from standardized Charpy notched impact test (CNIS) as to their relevance for material selection and design. 

It is now believed that the energy redistribution across the cross-section, instead of stress redistribution, reflects the physical processes connected with the mixed mode of failure more accurately. Hence, the use of an energy term Gc rather than a stress term in describing the mixed mode of failure appears to be physically more correct. The simple derivation of the relation between apparent critical strain energy release rate G/ and the two limiting values Gic and G can be found elsewhere (88). It is discussed in the following section in more detail. 

The fracture toughness is the measure of the damage tolerance of a matrix containing initial flaws or cracks. Gi<, and 620 are the critical strain energy release rates in the 1 and 2 directions respectively. Fracture toughness is expressed as the critical stress intensity factor as measured in ASTM E399. 

Gic is the critical strain energy release rate and y bt is the fracture surface energy of crack initiation, often referred to as the notched-beam-test fracture-surface energy in refractory literature. Also note that the stress intensity factor (Eq. 8.58) was given in Eq. (8.49) as ... 

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