representation of the strain vs. time curve (Fig. 45.8) suggests that a creep effect occurs. It comes out that waiting until the signal is stabilized would not achieve reasonable strain values for a residual stress calculation. If one represents the measured relaxed strain ‘εR’ due to the release of residual stresses as the sum of a time dependent component ‘εRt’ and a “spontaneous” constant component ‘εR0’, it would mean that we need this last elastic and time independent component ‘εR0’ to calculate the underlying residual stress. In Fig. 45.8 it should correspond to the first measured value at the time 0. But there is still another aspect which has to be taken into account. Figure 45.9 represents the strain measured during the same experiment, especially during the drilling process. Two SGRs spaced around 2 cm apart were bonded on the same specimen. Only one SGR was drilled. The solid line represents the result obtained while drilling the first gauge (drilled gauge), the dotted curve represents what was measured by the second gauge (undrilled gauge). The drilling process started at t ¼t1. It can be noticed that although only one SGR was drilled, a qualitatively similar signal could be measured on both of them. The observed strain gradient is too significant to be attributed to a local thermal effect. It is rather a purely mechanical effect due to the compression induced by the drilling tool while drilling. Indeed polypropylene has a strong viscoelastic behavior and, hence, the material creeps while being mechanically loaded. Based on this assumption the following model is used to obtain the component ‘εR0’ required to calculate residual stress. If the strain due to the compression effect of the drilling tool is called ‘εc’, then this strain can be decomposed as mentioned above in two strains: a time independent elastic component ‘εc0’ and a time dependent component ‘εct’. To explain the following point, it is considered that residual stresses are only released at the time t2 (end of the drilling process in Fig. 45.9), and not step by step while drilling. Based on the above mentioned assumptions it follows: ε tð Þ¼εc0, t ¼t1 ð45:1Þ While drilling, a viscoelastic effect is obtained because of the compressing effect of the drilling tool: ε tð Þ¼εc0 þεct t t1 ð Þ, t1 <t <t2 ð45:2Þ Finally just after drilling, strain release occurs caused by the release of residual stresses and due to elastic unloading, because the drilling tool is no more compressing the sample. Using the Boltzmann superposition principle (theory for linear viscoelasticity), the material keeps in memory the previous deformation, i.e. the viscoelastic part from the previous drilling tool compression (45.2): ε tð Þ¼εc0 þεct t2 t1 ð ÞþεR0 εc0, t ¼t2 ð45:3Þ ¼ ε tð Þ¼εct t2 t1 ð ÞþεR0, t ¼t2 ð45:4Þ Fig. 45.9 Strain measured on two strain gauge rosettes during the drilling process 45 Some Aspects of the Application of the Hole Drilling Method on Plastic Materials 379
RkJQdWJsaXNoZXIy MTMzNzEzMQ==