Ideal shear strength

One may attempt to derive the ideal shear strength So of the van der Waals solid normal to the chain axis from the value of the lateral surface free energy, a. This value is well known for common polymers such as PE or polystyrene (PS) (Hoffman et al, 1976) or else can be calculated from the Thomas-Stavely (1952) relationship a = /a Ahf)y, where a is the chain cross-section in the crystalline phase, Ahf is the heat of fusion, and y is a constant equal to 0.12. If one now assumes that a displacement between adjacent molecules by Si within the crystal is sufficient for lattice destruction then the ultimate transverse stress per chain will be given by So = cr/31. The values so obtained are shown in Table 2.1 for various polymers. In some cases (nylon, polyoxymethylene, polyoxyethylene (POE)) the agreement with experiment is fair. In the others, deviations are more evident. In order to understand better the discrepancy between the experimentally observed and the theoretically derived compressive strength one has to consider more thoroughly the micromorphology of polymer solids and the phenomena caused by the applied stress before lattice destruction occurs. 

Fig. 8.1. Representation of data for yield stress in a broad range of materials (adapted from Ashby and Jones (1996)). The npper limit is associated with the stress to induce plastic flow in the absence of defects and wiU be taken up in detail in our discussion of the ideal shear strength.

The ultimate resistance of a crystal, and hence the ideal shear strength, is the maximum value of r given by... 

Fig. 8.18. Model of stresses in core region of dislocation based upon the ideal shear strength. The elastically diverging stresses are cutoff for r < Vc on the assumption that the stresses within the core region have a constant value...

Zilibotti G, Righi MC (2011) Ab initio calculation of the adhesion and ideal shear strength of planar diamond interfaces with different atomic structure and hydrogen coverage. Langmuir 27 6862-6867... 

Idealized shear strength profiles for homogenous marine deposits that are (1) NC clay, (2) UC clay, and (3) OC clay are presented in Figure 8.31. A review of Figure 8.31a shows that the NC clay profile exhibits a linear shear strength behavior starting at zero at the... 

We note that if the ideal shear resistance of the (100) [001] plane system were given by a Frenkel sinusoid (Frenkel 1926) then the ideal shear strength of this system would be... 

Until now, most calculations of the theoretical strength of materials have been based on empirical or semiempirical interatomic potentials (for a review see e.g. Ref. 1 and the references therein ideal shear strengths for all basic cubic structures calculated by means of semiempirical potentials may be found in Ref. 2). However, these interatomic potentials are fitted to the properties of the equilibrium ground state and, therefore, it is not guaranteed that they are applicable when the material is loaded close to its theoretical strength limit, very far from the equilibrium state. 

Fig. 6. Ideal shear strength of Ta at its observed equilibrium volume fio> tis calculated by the PP and MGPT methods, (a) Symmetric energy barrier W(x, Qo) and (b) corresponding shear stress t(x, Qq).

Calculated ideal shear strength properties of Ta, Mo, and V at their observed equilibrium volumes, as obtained with the MGPT, FP-LMTO, and PP methods... 

The theoretical or ideal shear strength of any perfect crystal may be estimated using a method due originally to J. Frenkel (1926). He considered a crystal at absolute zero, neglected the zero-point energy, and assumed that, when slip occurs, all the molecules in one block of the crystal slide simultaneously over those in an adjacent block. 

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