Stored elastic strain energy

Assuming linear elastic behavior, the body can be viewed as a linear spring. The stored elastic strain energy U is given by the applied load (P) and the load-point displacement (A), or in terms of the compliance (C) of the body, or the inverse of its stiffness or spring constant i.e.. 

The above discussion indicates that TBCs can fail in a number of locations. Wherever a crack nucleates it will propagate if the stored elastic-strain energy exceeds the fracture toughness in that location. The mechanics of TBC failure have been reviewed in detail. The details of the fracture process depend on the type of bond coat and its fabrication, the technique for depositing the topcoat, and even on the nature of the thermal exposure (e.g., cycle frequency). ... 

Figure 8.1 shows stress-strain curves of atactic polystyrene (PS) in compression at 295 K for two structures with different initial states well annealed, i.e., furnace cooled from Tg + 20 K to room temperature, and rapidly quenched into ice water (Hasan and Boyce 1993). In both cases there is a gradual transition to fully developed plasticity that is reached at the peak of a yield phenomenon which is more prominent in the annealed material. Both curves show several unloading histories, starting with one close to the upper yield peak. All unloading paths show prominent Bauschinger effects of plastic strain recovery that is independent of the pre-strain. These indicate the presence of strain-induced back stresses and some recoverable stored elastic strain energy. In both cases the flow stress moves toward a unique flow state attained at a strain of around 0.3. 

Bridging of the crack by whiskers which stores elastic strain energy in the unfractured whisker. 

We now want to estimate the change dU ) in the stored elastic strain energy during crack propagation. To do this, we again consider the case of vanishing external work and assume a constant stress cr and a state of plane stress. Furthermore, we define a state 1 in which a stress (Tr is applied to the crack surfaces (see figure 5.7). At ctr = a, the crack is completely closed... 

The factor 2 is necessary because work is done on both sides of the crack. This process does not create any additional surface therefore AW is equal to the change in the stored elastic strain energy Using equation (5.3) yields... 

If the crack length increases by an amount da when a critical stress (Tc is applied, the stored elastic strain energy changes by... 

Now we load an identical plate until a force F is reached and afterwards keep the force constant (figure 5.9(b)). Again, the crack length is a. According to equation (5.20), the stored elastic strain energy is... 

Because of dA/da > 0, the stored elastic strain energy increases in this load case. During crack propagation by da, an external work AW = FA5 = F dX is done. The energy release rate can be calculated using equation (5.10) ... 

Fig. 13.2. stored elastic strain energy in the rubber bands in strain- and stress-controlled loading... 

Rp yield strength of materials with- [/(el) stored elastic strain energy... 

Fig. 3.3 GrifBth s model crack with a length of a, formed in a very thin plane-stressed plate causes release of stored elastic strain energy in the darkened area...

Single-edge crack Pure shear G = 2k aW, k njXt G, = IW, Ac = extension ratio at onset of crack growth Wc = critical stored elastic strain energy density 1 = initial length a,b,c a... 

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