Macroscopic yield stress

In this case, the glide layer propagates from the boundary into the cluster body, which leads to the nonuniform plastic deformation of a polycluster. Thus the macroscopic yield stress of a polycluster a, as it follows from (6.25), is determined by the relation... 

Figure 7. Tensile macroscopic yield stress of DGEBA-T403 epoxies as a function of T403 concentration, at 23 C.

Finite element modelling on a macroscopic scale using the Tresca criterion matches the observed size and shape of the plastic zone and also the shape of the indentation stress-strain curves indicating that the physical characteristics of the microstructure determine its yield strength. The use of the Tresca criterion implies a zero coefficient of friction on the microstructural scale. The range of macroscopic yield stresses for the materials studied here is 750 MPa to 2000 MPa. 

Finite element modelling on a microstructural scale indicates that internal yield has the appearance of a Mode II crack phenomenon (the shear strength of the microstructure depends on the inverse of the square root of the platelet diameter and is independent of the magnitude of the normal stress on the grain). There is a correlation between the macroscopic yield stress Y used in (2) above with the inverse square root of the grain size. 

The relevance to the present work is that the scale of contacts in the mica platelets studied here is in the order of 1 to 10 pm. This is the intermediate zone referred to by Johnson in which the frictional stress depends upon the inverse square root of the grain size in the manner of a Mode II crack. It has been previously shown that estimations of yield stress for a range of platelet sizes based on an inverse square root law yielded predictions of macroscopic behavior that agreed well with experimentally observed behavior and that the macroscopic yield stress was determined to be in the order of 1 GPa. A yield stress in the order of 1 GPa gives a value of So in the order of 500 MPa, precisely within the intermediate zone described above. The nature of the observed Mode II behaviour on the microstructural scale is thus explained. 

Now using the model suggested by the authors of Ref. [37] one can demonstrate that the clusters lose their stability, when stress in the polymer reaches the macroscopic yield stress, <5 Since the clusters are postulated as the set of densely packed collinear segments, and arbitrary orientation of cluster axes in relation to the applied tensile stress a should be expected, then they can be simulated as inclined plates (IP) [37], for which the following expression is true [37] ... 

The plastic constraint factor macroscopic yield stresses [32] ... 

Answer While an analysis of the actual stresses and dislocation movement in the complicated powder compact is not practical, we do know that in powder compacts of the particle size we have the stresses created by the surface tension can easily exceed the macroscopic yield stress of the material as the temperature is raised. There is a large literature (for example, the work by Gilman and Johnston) showing that the movement of dislocations is extremely sensitive to stress and temperature. The densification kinetics which we observe are in qualitative agreement with the kinetics of dislocation motion. 

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