Fracture Toughness Tests

Abstract

To apply the theory developed in the previous chapters, fracture toughness values must be measured. A wealth of methods for the determination of critical values of the stress intensity factor, R-curve, energy release rate have been developed. A number of these fracture toughness test methods are described here. The choice of method to use will depend on the material being tested and on your goals. Methods that work for steel will not work for composite materials. If you need data for a critical application you'll want to use a standard, accepted test method. If you are developing a new material and want to determine toughness as part of the development or screening process you might choose another method.

The role of sliding in ice stream formation

“…For a growing temperate region, we have V = ∂ y m /∂ t < 0, we assume that migration occurs only when heat flux is non-singular at y = y m (so there is no singular freezing rate false[−false(∂T/∂zfalse)false]−+) as previously studied in [11,12,16,19]: limyfalse→ym+(false|ym−y|1/2[∂T∂z]−+)≥01em if V<0. Note that the local analysis around the transition point y = y m in [19] is applicable here, which shows freezing will in general occur near the margin, but we can insist that freezing rates not be singular if the ice stream is expanding (in which case the left-hand side of (2.25) is zero, see also §2 of the electronic supplementary material). The condition (2.25) is mathematically analogous to prescribing a vanishing fracture toughness in crack propagation problems [36], although applied to the thermal rather than the mechanical problem. The condition must be stated explicitly as part of the model since one could otherwise construct a solution purely mathematically in which heat is siphoned out of the temperate region adjacent to the free boundary while the temperate region is widening: in other words, a locally infinite rate of basal freezing occurs in these solutions adjacent to the edge of a widening region of temperate bed, with the frozen-on water supplied by the basal drainage system (see electronic supplementary material, §S2).…”

Contribution of Unbroken Strands to the Fracture of Polymer Networks

“…The lifetime and utility of polymer networks are often restricted by their fracture, which involves the mechanical scission of covalent polymer strands within the network. The fracture of networks is typically discussed in terms of its tearing energy, which quantifies the resistance of a network to crack propagation. − The tearing energy has a critical value, which is defined by the minimum energy required to create a unit of the new surface. ,, Due to the lack of direct characterization of molecular behaviors at the crack tip, the energy required to break each bridging strand in the network that enters the critical tearing energy of the network remains unclear. − Hence, a quantitative molecular model that can provide physical and chemical insight into the molecular behaviors at the crack tip is needed for a detailed description of the fracture of polymer networks. The critical tearing energy of polymer networks has been extensively studied using the approach of fracture mechanics in which the network is usually considered as an elastic continuum .…”

“…The fracture of networks is typically discussed in terms of its tearing energy, which quantifies the resistance of a network to crack propagation. − The tearing energy has a critical value, which is defined by the minimum energy required to create a unit of the new surface. ,, Due to the lack of direct characterization of molecular behaviors at the crack tip, the energy required to break each bridging strand in the network that enters the critical tearing energy of the network remains unclear. − Hence, a quantitative molecular model that can provide physical and chemical insight into the molecular behaviors at the crack tip is needed for a detailed description of the fracture of polymer networks. The critical tearing energy of polymer networks has been extensively studied using the approach of fracture mechanics in which the network is usually considered as an elastic continuum . On small length scales, however, the network cannot be described as a continuous elastic body since it consists of tree-like structures of polymer chains that are “liquid-like”; the relevant length scale of this transition from continuum to molecular behavior is given by the topological loop size. , Current molecular models that estimate the network critical tearing energy mainly take into account only the energy of ruptured polymer strands (strands that originally bridge the crack interface) under crack propagation, ,, but they often ignore the role of the remainder of the tree-like structure , within the characteristic topological loop. , In the next few paragraphs, we first introduce both the macroscopic viewpoint that has been well established in fracture mechanics and review the molecular models that have been developed to estimate the critical tearing energy.…”

“…The critical tearing energy of polymer networks has been extensively studied using the approach of fracture mechanics in which the network is usually considered as an elastic continuum. 3 On small length scales, however, the network cannot be described as a continuous elastic body since it consists of tree-like structures of polymer chains that are "liquid-like"; the relevant length scale of this transition from continuum to molecular behavior is given by the topological loop size. 8,9 Current molecular models that estimate the network critical tearing energy mainly take into account only the energy of ruptured polymer strands (strands that originally bridge the crack interface) under crack propagation, 1,5,10 but they often ignore the role of the remainder of the tree-like structure 6,11 within the characteristic topological loop.…”

“…Macromolecules pubs.acs.org/Macromolecules Article https://doi.org/10.1021/acs.macromol.2c02139 Macromolecules XXXX, XXX, XXX−XXX C T h i s c o n t e n t i s o n l y l i c e n s e d f o r c o n s u m p t i o n b y A u t h o r i z e d U s e r s a f f i l i a t e d w i t h s c i t e . U s a g e b y a n y i n d i v i d u a l n o t d i r e c t l y a s s o c i a t e d w i t h s c i t e i s p r o h i b i t e d .The combined energy stored in all (z − 1) |g| chains of generation g is(3) …”