Pellejer et al 2023a - Revision history

Marherna at 14:48, 17 October 2023

2023-10-17T14:48:05Z

Marherna: Marherna moved page Review 333618240989 to Pellejer et al 2023a

2023-08-29T09:31:41Z

Marherna moved page Review 333618240989 to Pellejer et al 2023a

OswaldoAlejandroPellejer: Reference style

2023-06-20T09:39:02Z

Reference style

OswaldoAlejandroPellejer: /* References */

2023-06-20T09:32:40Z

‎References

OswaldoAlejandroPellejer at 13:20, 26 May 2023

2023-05-26T13:20:26Z

OswaldoAlejandroPellejer at 13:16, 26 May 2023

2023-05-26T13:16:28Z

OswaldoAlejandroPellejer: OswaldoAlejandroPellejer moved page Draft Pellejer 115108660 to Review 333618240989

2023-05-23T01:32:42Z

OswaldoAlejandroPellejer moved page Draft Pellejer 115108660 to Review 333618240989

OswaldoAlejandroPellejer at 01:23, 23 May 2023

2023-05-23T01:23:02Z

OswaldoAlejandroPellejer at 01:19, 23 May 2023

2023-05-23T01:19:49Z

OswaldoAlejandroPellejer at 01:17, 23 May 2023

2023-05-23T01:17:45Z

@@ Line 4: / Line 4: @@
 '''O.A. Pellejer<sup>a,b</sup>, A. Fernandez<sup>a</sup>, L. Cui<sup>b</sup>'''
 -->
 ==1 Introduction==

@@ Line 317: / Line 317: @@
 ==References==
-<br />[1] S. W. Tsai and E. M. Wu, «Journal of Composite Materials,» A general theory of strength for anisotropic materials, vol. 5, no. 1, pp. 58–80, 1971.
+<br />[1] S. W. Tsai and E. M. Wu, «Journal of Composite Materials,» ''A general theory of strength for anisotropic materials'', vol. 5, no. 1, pp. 58–80, 1971.
 DOI: 10.1177/002199837100500106.
-<br />[2] S. W. Tsai, «Think Composites,» Theory of Composite Design, 1992, ISBN: 0-9618090-3-5.
+<br />[2] S. W. Tsai, «Think Composites,» ''Theory of Composite Design'', 1992, ISBN: 0-9618090-3-5.
-<br />[3] I. I. Gol’denblat and V. A. Kopnov, «Polymer Mechanics,» Strength of glass-reinforced plastics in the complex stress state, vol. 1, pp. 54–59, 1965.
+<br />[3] I. I. Gol’denblat and V. A. Kopnov, «Polymer Mechanics,» ''Strength of glass-reinforced plastics in the complex stress state'', vol. 1, pp. 54–59, 1965.
-<br />[4] E. Ashkenaz, «Polymer Mechanics,» Problems of the anisotropy of strength, vol. 1, 60–70, 1965. DOI: 10.1007/BF00860686.
+<br />[4] E. Ashkenaz, «Polymer Mechanics,» ''Problems of the anisotropy of strength'', vol. 1, 60–70, 1965. DOI: 10.1007/BF00860686.
-<br />[5] S. W. Tsai and J. D. D. Melo, «Stanford Aeronautics & Astronautics,» Composite Materials Design and Testing: Unlocking mystery with invariants, 2015, ISBN: 978-0-9860845-0-8.
+<br />[5] S. W. Tsai and J. D. D. Melo, «Stanford Aeronautics & Astronautics,» ''Composite Materials Design and Testing: Unlocking mystery with invariants'', 2015, ISBN: 978-0-9860845-0-8.
-<br />[6] Composite Materials Handbook, «SAE International,» CMH-17, Volume 1: Polymer Matrix Composites: Guidelines for Characterization of Structural Materials, 2017, ISBN: 978-0-7680-9145-8.
+<br />[6] Composite Materials Handbook, «SAE International,» ''CMH-17, Volume 1: Polymer Matrix Composites: Guidelines for Characterization of Structural Materials'', 2017, ISBN: 978-0-7680-9145-8.

@@ Line 317: / Line 317: @@
 ==References==
-<br />[1] S. W. Tsai and E. M. Wu, “A general theory of strength for anisotropic materials,” Journal of Composite Materials, vol. 5, no. 1, pp. 58–80, 1971.
+<br />[1] S. W. Tsai and E. M. Wu, «Journal of Composite Materials,» A general theory of strength for anisotropic materials, vol. 5, no. 1, pp. 58–80, 1971.
-doi: 10.1177/002199837100500106.
+DOI: 10.1177/002199837100500106.
-<br />[2] S. W. Tsai, Theory of Composite Design. Think Composites, 1992, isbn: 0-9618090-3-5.
+<br />[2] S. W. Tsai, «Think Composites,» Theory of Composite Design, 1992, ISBN: 0-9618090-3-5.
-<br />[3] I. I. Gol’denblat and V. A. Kopnov, “Strength of glass-reinforced plastics in the complex stress state,” Polymer Mechanics, vol. 1, pp. 54–59, 1965.
+<br />[3] I. I. Gol’denblat and V. A. Kopnov, «Polymer Mechanics,» Strength of glass-reinforced plastics in the complex stress state, vol. 1, pp. 54–59, 1965.
-<br />[4] E. Ashkenaz, “Problems of the anisotropy of strength,” Polymer Mechanics, vol. 1, 60–70, 1965. doi: https://doi.org/10.1007/BF00860686.
+<br />[4] E. Ashkenaz, «Polymer Mechanics,» Problems of the anisotropy of strength, vol. 1, 60–70, 1965. DOI: 10.1007/BF00860686.
-<br />[5] S. W. Tsai and J. D. D. Melo, Composite Materials Design and Testing: Unlocking mystery with invariants. Stanford Aeronautics & Astronautics, 2015, isbn: 978-0-9860845-0-8.
+<br />[5] S. W. Tsai and J. D. D. Melo, «Stanford Aeronautics & Astronautics,» Composite Materials Design and Testing: Unlocking mystery with invariants, 2015, ISBN: 978-0-9860845-0-8.
-<br />[6] C. M. H. CMH-17, Volume 1: Polymer Matrix Composites: Guidelines for Characterization of Structural Materials. SAE International, 2017, isbn: 978-0-7680-9145-8.
+<br />[6] Composite Materials Handbook, «SAE International,» CMH-17, Volume 1: Polymer Matrix Composites: Guidelines for Characterization of Structural Materials, 2017, ISBN: 978-0-7680-9145-8.

@@ Line 190: / Line 190: @@
 where it can be proven that <math display="inline">F_{12\mathrm{,4L}}^{*} < F_{12\mathrm{,4U}}^{*}</math>
-Tsai [2] determined graphically the range of admissible values for <math display="inline">F_{12}</math> for some composite laminae by plotting <math display="inline">F_{12}</math> as a function of the slope at each of the anchor points. Figure [[#img-3|3]] shows the range of admissible values for <math display="inline">F_{12}</math> for the same composite laminae but determined with Eq.[[#eq-7|(7)]] to [[#eq-14|(14)]]. The ranges of admissible values found look alike the ones shown in Tsai and Melo [5] but something went unnoticed for the Kevlar/epoxy lamina. For this specific lamina, the upper limit (<math display="inline">F_{12\mathrm{,4U}}^{*} = -0.48</math>) is less than the lower limit (<math display="inline">F_{12\mathrm{,1aL}}^{*} = -0.33</math>), which means that it is not possible to meet failure mode interaction assumptions 1a and 4 together.
+Tsai [2] determined graphically the range of admissible values for <math display="inline">F_{12}^*</math> for some composite laminae by plotting <math display="inline">F_{12}^*</math> as a function of the slope at each of the anchor points. Figure [[#img-3|3]] shows the range of admissible values for <math display="inline">F_{12}^*</math> for the same composite laminae but determined with Eq.[[#eq-7|(7)]] to [[#eq-14|(14)]]. The ranges of admissible values found look alike the ones shown in Tsai and Melo [5] but something went unnoticed for the Kevlar/epoxy lamina. For this specific lamina, the upper limit (<math display="inline">F_{12\mathrm{,4U}}^{*} = -0.48</math>) is less than the lower limit (<math display="inline">F_{12\mathrm{,1aL}}^{*} = -0.33</math>), which means that it is not possible to meet failure mode interaction assumptions 1a and 4 together.
 <div id='img-3'></div>

@@ Line 68: / Line 68: @@
 |}
-The only remaining term to be defined is the interaction term <math display="inline">F_{12}</math>, which is related to the interaction of two stress components. This terms can be determined by an infinite number of combined stresses. Different experimental tests have been proposed [1], [3], [4] to find <math display="inline">F_{12}</math> but they are difficult to perform and, usually, empirical expressions are used instead.
+The only remaining term to be defined is the interaction term <math display="inline">F_{12}</math>, which is related to the interaction of two stress components. This term can be determined by an infinite number of combined stresses. Different experimental tests have been proposed [1], [3], [4] to find <math display="inline">F_{12}</math> but they are difficult to perform and, usually, empirical expressions are used instead.
 ==3 Unidirectional lamina==

← Older revision	Revision as of 09:31, 29 August 2023
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← Older revision	Revision as of 01:32, 23 May 2023
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 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
-|[[Image:Draft_Pellejer_115108660-InteractionModes.png|269px|Failure mode interactions (after Tsai1992).
+|[[File:Draft_Pellejer_115108660_5330_InteractionModes.svg|269px|Failure mode interactions (after Tsai1992).
 f(σ₁,σ₂) = F₁σ₁+F₂σ₂+F₁₁σ₁²+F₂₂σ₂²+2F₁₂σ₁σ₂

@@ Line 284: / Line 284: @@
 <div id='img-4'></div>
-{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 40%;max-width: 100%;"
+{| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 65%;max-width: 100%;"
 |-
 |[[File:Draft_Pellejer_115108660_3987_ExampleUD.svg|482px|Example: Tsai-Wu failure envelopes (τ₁₂=0)