Strain path

Collectively, the shock/release sequence amounts to a single cycle stress/ strain path change excursion with elastic and plastic deformation operative during both loading and unloading. 

Shock-recovery experiments by Gray [10] were conducted to assess directly if the strain-path reversal inherent to the shock contains a traditional microstructurally controlled Bauschinger effect for a shock-loaded two-phase material. Two samples of a polycrystalline Al-4 wt.% Cu alloy were shock loaded to 5.0 GPa and soft recovered in the same shock assembly to assure identical shock-loading conditions. The samples had two microstructural... 

Path A is disfavored because it produces a secondary carbocation. It is favored because the five-membered rings that are formed have lower ring strain. Path B is favored because it produces a tertiary carbocation. It is disfavored due to the strain in the four-membered ring of the product. 

In Eqn. (12), rd represents the dynamic interfacial shear stress, which may differ from that which would be measured from fiber push-out experiments, which are typically conducted at low sliding velocities. Equation (12) holds for partial sliding along the interface. When the minimum applied stress is equal to zero, the area of the hysteresis loop can also be calculated as the integral from zero to (Tmax of the difference between the strain paths for loading and unloading (Eqns. (3) and (4)) ... 

Continuous strain without change of strain path,... 

Key words Severe plastic deformation, strain path, fragmentation, geometric recovery, strain efficiency, equivalent strain... 

A number of SPD techniques have been developed (for a survey see [8]). They can be classified by their strain paths ... 

For a discussion of SPD without change of strain path a rough estimate of equivalent strains using, e.g., a =2 may be reasonable. Caution is necessary when strain is accumulated with changing strain path. This is so because there is no reason to believe that the total plastic work put into a material is a sufficient measure to determine its microstructure (for a more detailed discussion, see [10]). 

Accumulated Strain with Reversal of Strain Path... 

This value has been used as abscissa for the stress/strain curve in fig.5. Fig.6 shows a corresponding curve obtained without change of strain path. It shows the well-known stages HI, IV and V. Fig.5 has been similarly divided into stages B, C and D. Careful investigations of microstructure [3,11] have shown that stages B, C and D correspond to II, IV and V. Comparison of the onset strains shows that the strain defined by eq.(4) is much less efficient to produce the corresponding structures. It should therefore be corrected by an efficiency factor r so that... 

Figure 6. Stress-strain curve for AlMg5 deformed without change of strain path [11]...

The importance of geometric recovery is quite plausible when the strain path is reversed. It is not so obvious when the strain path changes in more complicated ways. Experiments on the cold swaging of copper [10,12,13] indicate that geometric recovery is also important for an irregular sequence of strain paths. This problem should therefore be looked at more closely for ECA-pressing. 

For a comparison of the efficiency of different SPD techniques to produce such structures the traditional concept of equivalent strain based on equal mechanical work is problematic, especially when strain is accumulated in steps with varying strain path where geometric recovery must be taken into account. 

Li S, Li Y and Wu Z. 1995. The Permeability-strain equation relating to complete stress-strain path of the rock. Chinese J. of Geotech. Engng., 17(2), pp. 13-19. 

Jiang Zhenquan and Ji Liangjun, 2001, The laboratory study on behavior of permeability of rock along the complete stress-strain path. 

As mentioned above, the calculatimi for a given strain increment is the key to calculate the backstress-tensor a for a defined strain path because... 

It is necessary to deform the specimen along a linear strain path, i.e., the trajectory followed by a point in the Ei, E2 plane until reaching the forming limit must be a straight line. Although several tests have been developed in the past, Nakazima s one is commonly utilized in practice. 

The complex strain paths undergone by industrial parts during multi-pass forming can be simulated in laboratory tests by applying to the same specimen successively two different load paths, for example, a tensile test followed by deep drawing or biaxial expansion followed by a local tensile test. The analysis of the specimens provides results similar to those for real industrial components ... 

The most important influence is due to the modification of the strain path. More details about the factors influencing the FLC are presented in the reference (Banabic 2000, 2010 Banabic et al. 2010). 

The formability limits of a sheet metal were described by Keeler in the form of a forming limit diagram (FLD) [771. FLDs are dependent on bulk material properties, geometry of deformation, strain history (or strain path), sheet thickness, and the characteristics of the tool-sheet interface. Thus, the FLD acts only as an indicator of formability and cannot be regarded as a material property 178]. 

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