Academia.eduAcademia.edu

Figure 1 – uploaded by Christos Michail

See full PDFdownloadDownload figure
Fic. 1. (a) Engineering drawing of the testpiece showing plan and side elevation views; scrapview detail @ is given in (b). (b) Engineering drawing of the testpiece showing details of a slitted extensometer ridge. The scrapview detail is given in (a).

Figure 1 Fic. 1. (a) Engineering drawing of the testpiece showing plan and side elevation views; scrapview detail @ is given in (b). (b) Engineering drawing of the testpiece showing details of a slitted extensometer ridge. The scrapview detail is given in (a).

Related Figures (15)

Fic. 2. Photograph of slitted extensometer ridge.
Fic. 2. Photograph of slitted extensometer ridge.
Fic. 11. Field plots of the damage variable w,. at the time fraction t/t, = 0.999 for four different testpieces. The letters A and B denote gauge lengths of 50 and 10 mm, respectively. The lower case identifiers -s and -us denote slitted and unslitted extensometer ridges, respectively.
Fic. 11. Field plots of the damage variable w,. at the time fraction t/t, = 0.999 for four different testpieces. The letters A and B denote gauge lengths of 50 and 10 mm, respectively. The lower case identifiers -s and -us denote slitted and unslitted extensometer ridges, respectively.
Fic. 12. Variation of normalised effective creep strain field 4, at the time fraction t/t, = 0.700 for four different testpieces. The letters A and B denote gauge lengths of 50 and 10 mm, respectively. The lower case identifiers -s and -us denote slitted and unslitted extensometer ridges, respectively.
Fic. 12. Variation of normalised effective creep strain field 4, at the time fraction t/t, = 0.700 for four different testpieces. The letters A and B denote gauge lengths of 50 and 10 mm, respectively. The lower case identifiers -s and -us denote slitted and unslitted extensometer ridges, respectively.
Fic. 3. Experimental and theoretical creep curves obtained for unslitted ridged testpieces with gauge length of 50mm. The continuous lines denote experimental results and the broken lines denote theoretical predictions. The numbers given for each curve refer to stress levels in MPa.
Fic. 3. Experimental and theoretical creep curves obtained for unslitted ridged testpieces with gauge length of 50mm. The continuous lines denote experimental results and the broken lines denote theoretical predictions. The numbers given for each curve refer to stress levels in MPa.
Fic. 4. Comparison of experimental creep curves for unslitted ridged testpieces with different gauge lengths obtained at the same stress level of 250.0 MPa. The numbers given on the figure denote testpiece gauge lengths of 50, 30 and 10 mm.
Fic. 4. Comparison of experimental creep curves for unslitted ridged testpieces with different gauge lengths obtained at the same stress level of 250.0 MPa. The numbers given on the figure denote testpiece gauge lengths of 50, 30 and 10 mm.
Fic. 5. Comparison of experimental creep curves for unslitted and slitted ridged testpieces denoted by continuous and broken lines, respectively, for tests carried out at the stress level of 250.0 MPa. The numbers given on the figure denote the gauge lengths of 50, 30 and 10 mm.
Fic. 5. Comparison of experimental creep curves for unslitted and slitted ridged testpieces denoted by continuous and broken lines, respectively, for tests carried out at the stress level of 250.0 MPa. The numbers given on the figure denote the gauge lengths of 50, 30 and 10 mm.
The form of the constitutive equations for multi-axial conditions are given by the following equation set: tri-axial stress-state generated at the notch. This usually does not present severe difficulties since the degree of necking required to produce significant tri-axial stress is large, and this does not take place until the final stages of the test, and can therefore often be neglected. In all specimens tested in this investigation no necking took place; and hence these complica- tions were not encountered. The equation set contains two damage state variables used to model tertiary softening mechanisms. The first damage state variable, ®, which is described by the third equation in set (1), is defined from the physics of ageing to lie within the range 0-1 for mathematical convenience. The second damage variable, w,, defined by the fourth equation in set (1), describes grain boundary creep constrained cavitation, the magnitude of which is strongly sensitive to alloy composition and to processing route. Creep constrained cavitation can either be nucleation or growth controlled. In this paper, only nucleation control will be considered. Using a nucleation rate model which is linear in strain rate; proportional to the stress parameter (c,/c.)’: and a failure criterion of w>, = 1/3 gives:
The form of the constitutive equations for multi-axial conditions are given by the following equation set: tri-axial stress-state generated at the notch. This usually does not present severe difficulties since the degree of necking required to produce significant tri-axial stress is large, and this does not take place until the final stages of the test, and can therefore often be neglected. In all specimens tested in this investigation no necking took place; and hence these complica- tions were not encountered. The equation set contains two damage state variables used to model tertiary softening mechanisms. The first damage state variable, ®, which is described by the third equation in set (1), is defined from the physics of ageing to lie within the range 0-1 for mathematical convenience. The second damage variable, w,, defined by the fourth equation in set (1), describes grain boundary creep constrained cavitation, the magnitude of which is strongly sensitive to alloy composition and to processing route. Creep constrained cavitation can either be nucleation or growth controlled. In this paper, only nucleation control will be considered. Using a nucleation rate model which is linear in strain rate; proportional to the stress parameter (c,/c.)’: and a failure criterion of w>, = 1/3 gives:
The equations will be used together with the effective stress multi-axial rupture criterion for the aluminium alloy, given by r = 0, as discussed by Kowalewski et al. [4]. The equations have been used to determine the time variation of the stress, strain and damage fields within the testpieces, and the techniques used are discussed in the following section.
The equations will be used together with the effective stress multi-axial rupture criterion for the aluminium alloy, given by r = 0, as discussed by Kowalewski et al. [4]. The equations have been used to determine the time variation of the stress, strain and damage fields within the testpieces, and the techniques used are discussed in the following section.
Fic. 7. Variation of the R-ratio with the time fraction t/t, for the testpiece with extensometer ridges without slits determined using DAMAGE XxX, for o = 250 MPa. The continuous line denotes the R-ratios used to correct the experimental creep curves presented in Fig. 3 in the first iteration. The broken line denotes the R-ratios used in the second correction of the experimental creep curves presented in Fig. 3. The chain line, upper curve, denotes the R-ratios used in the final correction of the original experimental data shown in Fig. 3. Seine Keelearne eaten: aim «cles sles sven wets nn a ee The continuous R- t/t curve given in Fig. 7 has then been used to correct the experimental creep curves presented in Fig. 3, with the objective of generating a set of creep curves which are closer to the true curves for the aluminium alloy. The new set of creep
Fic. 7. Variation of the R-ratio with the time fraction t/t, for the testpiece with extensometer ridges without slits determined using DAMAGE XxX, for o = 250 MPa. The continuous line denotes the R-ratios used to correct the experimental creep curves presented in Fig. 3 in the first iteration. The broken line denotes the R-ratios used in the second correction of the experimental creep curves presented in Fig. 3. The chain line, upper curve, denotes the R-ratios used in the final correction of the original experimental data shown in Fig. 3. Seine Keelearne eaten: aim «cles sles sven wets nn a ee The continuous R- t/t curve given in Fig. 7 has then been used to correct the experimental creep curves presented in Fig. 3, with the objective of generating a set of creep curves which are closer to the true curves for the aluminium alloy. The new set of creep
TABLE 1. TRUE MATERIAL CONSTANTS curves which resulted from this process were then used as input to the optimisation scheme reported by Kowalewski et al. [4] to redetermine the constitutive parameters. The consti- tutive parameters so determined were then used in the solver DAMAGE XxX to generate the second R-t/t, curve shown by the broken line in Fig. 7. This second curve was then used to recorrect the original experimental creep curve shown in Fig. 3, and the process repeated to produce the third R — t/t; curve which is shown by the chain line in Fig. 7. It may be observed that the second and third R — t/t; curves are almost identical except for small errors in the latter stages, 0.4 < t/t, < 1.0, of the curve. If a further correction was to be carried out, then the corrections to be made to the original creep curves of Fig. 3 would be negligible. The process may therefore be considered to have converged and the true constitutive parameters obtained, for which the constants are given in Table 1. The final modifications to the experimental creep curves given in Fig. 3 are shown in Fig. 8 by the continuous lines, and the broken lines denote the predictions made by the fitted data listed in Table |. The true constitutive equations, given by Eqns (1) and the data of Table 1, will be used in the following subsections to predict the behaviour of the unslitted and slitted ridged testpieces.
TABLE 1. TRUE MATERIAL CONSTANTS curves which resulted from this process were then used as input to the optimisation scheme reported by Kowalewski et al. [4] to redetermine the constitutive parameters. The consti- tutive parameters so determined were then used in the solver DAMAGE XxX to generate the second R-t/t, curve shown by the broken line in Fig. 7. This second curve was then used to recorrect the original experimental creep curve shown in Fig. 3, and the process repeated to produce the third R — t/t; curve which is shown by the chain line in Fig. 7. It may be observed that the second and third R — t/t; curves are almost identical except for small errors in the latter stages, 0.4 < t/t, < 1.0, of the curve. If a further correction was to be carried out, then the corrections to be made to the original creep curves of Fig. 3 would be negligible. The process may therefore be considered to have converged and the true constitutive parameters obtained, for which the constants are given in Table 1. The final modifications to the experimental creep curves given in Fig. 3 are shown in Fig. 8 by the continuous lines, and the broken lines denote the predictions made by the fitted data listed in Table |. The true constitutive equations, given by Eqns (1) and the data of Table 1, will be used in the following subsections to predict the behaviour of the unslitted and slitted ridged testpieces.
Fic. 8. Comparison of creep curves obtained from data originally presented in Fig. 3, corrected for errors due to the presence of extensometer ridges, with theoretical predictions made using Eqns (1) with the true constitutive parameters. The continuous lines denote the final correction to the original experimental data, and the broken lines denote the theoretical predictions.
Fic. 8. Comparison of creep curves obtained from data originally presented in Fig. 3, corrected for errors due to the presence of extensometer ridges, with theoretical predictions made using Eqns (1) with the true constitutive parameters. The continuous lines denote the final correction to the original experimental data, and the broken lines denote the theoretical predictions.
Fic. 10. Comparison of creep curves for slitted ridged specimens of different gauge lengths com- puted from the extensometer displacements using the solver DAMAGE XxX (broken lines), with the experimental creep curves (continuous lines). The numbers given on the figure denote the gauge lengths of 50. 30 and 10 mm. All creep curves are for the stress level of 250 MPa. Fic. 9. Comparison of creep curves for unslitted ridged testpieces of 50, 30 and 10 mm gauge lengths under the stress level of 250 MPa, computed from the extensometer displacement using the solver DAMAGE XxX (broken lines), with the experimental curves presented previously in Fig. 4.
Fic. 10. Comparison of creep curves for slitted ridged specimens of different gauge lengths com- puted from the extensometer displacements using the solver DAMAGE XxX (broken lines), with the experimental creep curves (continuous lines). The numbers given on the figure denote the gauge lengths of 50. 30 and 10 mm. All creep curves are for the stress level of 250 MPa. Fic. 9. Comparison of creep curves for unslitted ridged testpieces of 50, 30 and 10 mm gauge lengths under the stress level of 250 MPa, computed from the extensometer displacement using the solver DAMAGE XxX (broken lines), with the experimental curves presented previously in Fig. 4.
Fic. 13. Comparison of the variation of the R-ratio with the time fraction 1 1, for the slitted and unslitted ridged testpieces with different gauge lengths obtained by using the solver DAMAGE XX for o = 250 MPa. The continuous lines denote R-ratios for unslitted ridged specimens, the broken lines denote R-ratios for slitted ridged specimens. The numbers given on the figure denote the gauge lengths of 50, 30 and 10 mm.
Fic. 13. Comparison of the variation of the R-ratio with the time fraction 1 1, for the slitted and unslitted ridged testpieces with different gauge lengths obtained by using the solver DAMAGE XX for o = 250 MPa. The continuous lines denote R-ratios for unslitted ridged specimens, the broken lines denote R-ratios for slitted ridged specimens. The numbers given on the figure denote the gauge lengths of 50, 30 and 10 mm.
Related topics:
Mechanical EngineeringCivil EngineeringBiomedical EngineeringDigital MammographyDigital RadiographyManufacturing EngineeringMechanical Engineering SciencesSemiconductor device modelingDetective Quantum EfficiencyInformation capacity
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved