Martin Beato et al 2024a - Revision history

Marherna: Marherna moved page Review 841175581933 to Martin Beato et al 2024a

2024-12-16T12:50:24Z

Marherna moved page Review 841175581933 to Martin Beato et al 2024a

Marherna at 12:49, 16 December 2024

2024-12-16T12:49:26Z

Jmbeato at 11:55, 19 July 2023

2023-07-19T11:55:10Z

Jmbeato at 09:32, 19 July 2023

2023-07-19T09:32:10Z

Jmbeato at 09:23, 19 July 2023

2023-07-19T09:23:10Z

Jmbeato at 07:34, 19 July 2023

2023-07-19T07:34:10Z

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Jmbeato: Replaced content with " == Abstract == == Full document == Media:Review_841175581933-5163-document.pdf"

2023-07-19T07:32:04Z

Replaced content with " == Abstract == == Full document == <pdf>Media:Review_841175581933-5163-document.pdf</pdf>"

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Jmbeato at 07:28, 19 July 2023

2023-07-19T07:28:16Z

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Jmbeato: small change in one stacking sequence that was wrong

2023-05-31T08:32:00Z

small change in one stacking sequence that was wrong

Jmbeato: Jmbeato moved page Draft Martin Beato 635931335 to Review 841175581933

2023-05-31T08:12:25Z

Jmbeato moved page Draft Martin Beato 635931335 to Review 841175581933

← Older revision		Revision as of 12:49, 16 December 2024
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−	~~<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">~~
−	~~<big>'''Estudio de la influencia del espesor de lámina y secuencia de laminado en las tensiones por efecto borde'''</big></div>~~
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−	~~<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">~~
−	~~<big>'''On the influence of ply thickness and stacking sequence in the Free-edge effect '''</big></div>~~
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−	~~<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">~~
−	~~'''J.Martín<sup>1</sup>*, J.M.González-Cantero<sup>1</sup>, S.Rebollo<sup>1</sup>, A. Torres<sup>1</sup>, D.Meizoso<sup>1</sup>, J.M.Blanco<sup>1</sup>, J.A.Rodriguez<sup>1</sup> '''</div>~~
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−	~~<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">~~
−	~~<sup>1</sup>AIRBUS Operaciones S.L.</div>~~
−
−	~~<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">~~
−	[mailto:jorge.j.martin-beato@airbus.com jorge.j.martin-beato@airbus.com], [mailto:juan-manuel.gonzalez-cantero@airbus.com juan-manuel.gonzalez-cantero@airbus.com], [mailto:sergio.rebollo-dabo@airbus.com sergio.rebollo-dabo@airbus.com], [mailto:antonio.a.torres-esteban@airbus.com antonio.a.torres-esteban@airbus.com], [mailto:daniel.meizoso@airbus.com daniel.meizoso@airbus.com] , [mailto:jose.ma.blanco@airbus.com jose.ma.blanco@airbus.com], [mailto:jose.e.rodriguez@airbus.com jose.e.rodriguez@airbus.com]</div>

	==1. Introduction==		==1. Introduction==

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 Free-edge effect is a stress concentration phenomenon that appears in the discontinuities of composite materials, such as edges, holes or corners. As it can be shown in the following example, see <span id='cite-figure1'></span>[[#figure1|Figure 1]], if we assume a stacking sequence such as [0/90/90/0], where the different layers are not bonded together, but just stacked, one on top of the other, if we apply to the stack a certain load in the <math display="inline">{x}_{1}</math> direction, every ply suffers a shrink in the transverse direction <math display="inline">\, {x}_{2}</math>, due to Poisson’s effect.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id="_GoBack" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
   [[Image:Review_841175581933-image1.png|600px]] </div>
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 <div id="figure3" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 Figure 3. 2D maps of stresses in MPa for a rectangular cross ply [45/-45]<sub>s</sub> section, under arbitrary axial load.</div>
 ==4. Validation process==

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 Free-edge effect is a stress concentration phenomenon that appears in the discontinuities of composite materials, such as edges, holes or corners. As it can be shown in the following example, see <span id='cite-figure1'></span>[[#figure1|Figure 1]], if we assume a stacking sequence such as [0/90/90/0], where the different layers are not bonded together, but just stacked, one on top of the other, if we apply to the stack a certain load in the <math display="inline">{x}_{1}</math> direction, every ply suffers a shrink in the transverse direction <math display="inline">\, {x}_{2}</math>, due to Poisson’s effect.
-<div id="_GoBack" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
   [[Image:Review_841175581933-image1.png|600px]] </div>
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-  [[Image:Review_841175581933-image2-c.PNG|600px]] </div>
+  [[Image:Review_841175581933-image2-c.png|600px]] </div>
 <div id="figure2" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-  [[Image:Review_841175581933-image3-c.PNG|600px]] </div>
+  [[Image:Review_841175581933-image3-c.png|600px]] </div>
 <div id="figure3" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
 Figure 3. 2D maps of stresses in MPa for a rectangular cross ply [45/-45]<sub>s</sub> section, under arbitrary axial load.</div>
 ==4. Validation process==

@@ Line 20: / Line 20: @@
 Free-edge effect is a stress concentration phenomenon that appears in the discontinuities of composite materials, such as edges, holes or corners. As it can be shown in the following example, see <span id='cite-figure1'></span>[[#figure1|Figure 1]], if we assume a stacking sequence such as [0/90/90/0], where the different layers are not bonded together, but just stacked, one on top of the other, if we apply to the stack a certain load in the <math display="inline">{x}_{1}</math> direction, every ply suffers a shrink in the transverse direction <math display="inline">\, {x}_{2}</math>, due to Poisson’s effect.
-<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div id="_GoBack" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-  [[Image:Review_841175581933-image1-c.PNG|600px]] </div>
+  [[Image:Review_841175581933-image1.png|600px]] </div>
 <div id="figure1" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 As it is described in detail in the paper of C Mittelstedt and W Becker, see <span id='cite-ref2'></span>[[#ref2|[2] ]], there are different ways to solve the edge effect problem. Classical laminate analysis cannot be used to capture the interlaminar stresses in a flat panel and the 3D constitutive equations for an orthotropic composite material lead to a complex set of differential equations that have not been solved yet. All the available solutions are based on some sort of simplifications that allow to obtain a solution close to the real problem. Based on the nature of the solution, methods can be separated in two different main groups:
-:* '''Closed-form solution''': In this group there are all the analytical methods that, based on some simplifications, obtain the interlaminar stresses, like the work of Puppo and Evensen, see <span id='cite-ref3'></span>[[#ref3|[3]]] or Pagano, mixing Mindlin laminate theory and finite element models <span id='cite-ref4'></span>[[#ref4|[4]]]. Most of the methods of this group provide a fast an accurate solution but it fails to cover a wide range of use cases. For instance, they are usually limited to the stacking sequences tested, as they are mainly intended for research purpose.
+:* '''Closed-form solution''': In this group there are all the analytical methods that, based on some simplifications, obtain the interlaminar stresses, like the work of Puppo and Evensen, see <span id='cite-ref3'></span>[[#ref3|[3]]] or Pagano, mixing Mindlin laminate theory and finite element models <span id='cite-ref4'></span>[[#ref4| ]]. Most of the methods of this group provide a fast an accurate solution but it fails to cover a wide range of use cases. For instance, they are usually limited to the stacking sequences tested, as they are mainly intended for research purpose.
 :* '''Finite Element models''': These model are well-known to solve solid mechanical problems and are able to predict free-edge effect with the proper element formulation and mesh refinement, so most of the works are focused on high order elements and meshing convergence strategy, see Vidal <span id='cite-ref5'></span>[[#ref5|[5]]]. Even if those methods can cover a wide range of stacking and loads, it requires a high amount of effort to set up the model, reducing the applicability for an industrial solution to be used for trade-offs and/or optimization.
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 The analytical modelling of the free-edge effects is analyzed in a flat laminate where the main load direction is defined as the X-coordinate, the width direction as the Y-coordinate and the through-the-thickness direction as the Z-coordinate, as it is shown in <span id='cite-figure2'></span>[[#figure2|Figure 2]]:
-<div id="_GoBack" class="center" style="width: auto; margin-left: auto; margin-right: auto;">
+<div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
   [[Image:Review_841175581933-image2-c.PNG|600px]] </div>

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 Nevertheless, analyzing only max values can lead to wrong interpretation of the real phenomena as the stresses depicted here are the value obtain at y =0.1mm of the edge, but they are related to a stress concentration effect and decrease far from the edges. As it can be shown in the first laminate, the amount of plies that are suffering a positive σ<sub>z</sub> (tensile) covers almost 6 plies, reaching its peak at the 90 ply, whereas in the second stacking, only the 90° ply is under interlaminar stresses and it decreases outside this ply. This fact it crucial in order to understand the area of the stacking that is affected from free-edge effect Ply thickness effect.
-Other interesting exercise can be performed when the ply thickness is modified: in this example two stacking with the same thickness and almost the same mechanical properties are compared. The main difference is in the ply thickness, the first stacking sequence has a cured ply thickness (CPT) of 0.25mm and a staking sequence: [45/0/-45/90/45/0/-45/90/45/0/-45/90], whereas second stacking is [45/0/-45/90/45/0/-45/90]s, of CPT 0.5 mm.
+Other interesting exercise can be performed when the ply thickness is modified: in this example two stacking with the same thickness and almost the same mechanical properties are compared. The main difference is in the ply thickness, the first stacking sequence has a cured ply thickness (CPT) of 0.25mm and a staking sequence: [45/0/-45/90/45/0/-45/90/45/0/-45/90], whereas second stacking is [45/0/-45/90/45/0/90/45/90/-45/0/45], of CPT 0.5 mm.
 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
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 <div class="center" style="width: auto; margin-left: auto; margin-right: auto;">
-Top results: [45/0/-45/90/45/0/-45/90/45/0/-45/90]s,  bottom [45/0/-45/90/45/0/-45/90]s.</div>
+Top results: [45/0/-45/90/45/0/-45/90/45/0/-45/90]s,  bottom [45/0/-45/90/45/0/90/45/90/-45/0/45].</div>
 As was previously described, main interlaminar stresses are located where 90° plies are. See Figure 9. Also, it can be noticed that as the ply thickness is duplicated, peak stress values are increase by ~18%, as one can expect higher values for higher CPT, based on previous the exercise, since the thick plies can be assumed to be equivalent to two thin plies.

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