Quasi Static Axial Compression of Thin Walled Aluminum Tubes: Analysis of Flow Stress in the Analytical Models
Authors: Yob Mohd Nizam , Ismail Khairul Azwan , Rojan M. A. , Othman Mohd Zaid , Ahmad Zaidi Ahmad Mujahid 
Published: January 2016

<p class="zhengwen"><span lang="EN-GB">This paper presents experimental work on quasi static compression tests on aluminum AA 6063 circular and square tubes. Specimen tubes with ratio of R/t = 12 and b/t = 24 for circular and square tubes respectively were prepared and validated with several analytical model developed by previous researchers. Two definitions of flow stress were used for validate the test result, first were proposed by Abramowicz and Jones </span><!--[if supportFields]><span lang=EN-GB style='mso-bidi-font-size:10.0pt'><span style='mso-element:field-begin; mso-field-lock:yes'></span>ADDIN CSL_CITATION { &quot;citationItems&quot; : [ { &quot;id&quot; : &quot;ITEM-1&quot;, &quot;itemData&quot; : { &quot;DOI&quot; : &quot;http://dx.doi.org/10.1115/1.3167137&quot;, &quot;abstract&quot; : &quot;A self-consistent theory is presented which describes the crushing behavior of a class of thin-walled structures. Assuming a rigid-plastic material and using the condition of kinematic continuity on the boundaries between rigid and deformable zones, a basic folding mechanism is constructed. This mechanism closely reproduces all the main features of folds and wrinkles actually observed on typical crumpled sheet metal structures. Calculations based on the energy balance postulate show that two-thirds of the plastic energy is always dissipated through inextensional deformations at stationary and moving plastic hinge lines. The extensional deformations are confined to relatively small sections of the shell surface but they account for the remaining one-third of the dissipated energy. The theory is illustrated by application to the problem of progressive folding of thin-walled rectangular columns. A good correlation is obtained with existing experimental data as far as the mean crushing force and the geometry of the local collapse mode is concerned.&quot;, &quot;author&quot; : [ { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Wierzbicki&quot;, &quot;given&quot; : &quot;T.&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; }, { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Abramowicz&quot;, &quot;given&quot; : &quot;W.&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; } ], &quot;container-title&quot; : &quot;Journal of Applied Mechanics (ASME)&quot;, &quot;id&quot; : &quot;ITEM-1&quot;, &quot;issued&quot; : { &quot;date-parts&quot; : [ [ &quot;1983&quot; ] ] }, &quot;page&quot; : &quot;727-734&quot;, &quot;title&quot; : &quot;On the crushing mechanics of thin walled structures&quot;, &quot;type&quot; : &quot;article&quot;, &quot;volume&quot; : &quot;50&quot; }, &quot;uris&quot; : [ &quot;http://www.mendeley.com/documents/?uuid=179d439b-63d5-4300-ac65-ecc43225d578&quot; ] } ], &quot;mendeley&quot; : { &quot;formattedCitation&quot; : &quot;(Wierzbicki &amp; Abramowicz, 1983)&quot;, &quot;plainTextFormattedCitation&quot; : &quot;(Wierzbicki &amp; Abramowicz, 1983)&quot;, &quot;previouslyFormattedCitation&quot; : &quot;(Wierzbicki &amp; Abramowicz, 1983)&quot; }, &quot;properties&quot; : { &quot;noteIndex&quot; : 0 }, &quot;schema&quot; : &quot;https://github.com/citation-style-language/schema/raw/master/csl-citation.json&quot; }<span style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-GB">(Wierzbicki &amp; Abramowicz, 1983)</span><!--[if supportFields]><span lang=EN-GB style='mso-bidi-font-size:10.0pt'><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-GB">, defined as mean stress between yield stress and ultimate tensile stress. Secondly, using ultimate tensile stress as flow stress. For circular tubes test result is in better agreement with the analytical model by Guillow et al. </span><!--[if supportFields]><span lang=EN-GB style='mso-bidi-font-size:10.0pt'><span style='mso-element:field-begin; mso-field-lock:yes'></span>ADDIN CSL_CITATION { &quot;citationItems&quot; : [ { &quot;id&quot; : &quot;ITEM-1&quot;, &quot;itemData&quot; : { &quot;DOI&quot; : &quot;http://dx.doi.org/10.1016/S0020-7403(01)00031-5&quot;, &quot;abstract&quot; : &quot;This paper presents further experimental investigations into axial compression of thin-walledcircular tubes, a classical problem studied for several decades. A total of 70 quasi-static tests were conducted on circular 6060 aluminium tubes in the T5, as-receivedcondition. The range of D=t considered was expanded over previous studies to D=t=10\u2013450. Collapse modes were observed for L=D610 anda mode classi?cation chart developed. The average crush force, FAV, was non-dimensionalisedandan empirical formula establishedas FAV=MP =72:3(D=t)0:32. It was foundthat test results for both axi-symmetric and non-symmetric modes lie on a single curve. Comprehensive comparisons have been made between existing theories andour test results for FAV. This has revealedsome shortcomings, suggesting that further theoretical work may be required. It was found that the ratio of FMAX=FAV increasedsubstantially with an increase in the D=t ratio. The e?ect of ?lling aluminium tubes with di?erent density polyurethane foam was also brie?y examined. ?&quot;, &quot;author&quot; : [ { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Guillow&quot;, &quot;given&quot; : &quot;S R&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; }, { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Lu&quot;, &quot;given&quot; : &quot;G&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; }, { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Grzebieta&quot;, &quot;given&quot; : &quot;R H&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; } ], &quot;container-title&quot; : &quot;International Journal of Mechanical Sciences&quot;, &quot;id&quot; : &quot;ITEM-1&quot;, &quot;issued&quot; : { &quot;date-parts&quot; : [ [ &quot;2001&quot; ] ] }, &quot;page&quot; : &quot;2103-2123&quot;, &quot;title&quot; : &quot;Quasi-static axial compression of thin-walled circular aluminium tubes&quot;, &quot;type&quot; : &quot;article-journal&quot;, &quot;volume&quot; : &quot;43&quot; }, &quot;uris&quot; : [ &quot;http://www.mendeley.com/documents/?uuid=8c6bee51-14aa-4333-9e6c-d81b06c0470b&quot; ] } ], &quot;mendeley&quot; : { &quot;formattedCitation&quot; : &quot;(Guillow, Lu, &amp; Grzebieta, 2001)&quot;, &quot;plainTextFormattedCitation&quot; : &quot;(Guillow, Lu, &amp; Grzebieta, 2001)&quot;, &quot;previouslyFormattedCitation&quot; : &quot;(Guillow, Lu, &amp; Grzebieta, 2001)&quot; }, &quot;properties&quot; : { &quot;noteIndex&quot; : 0 }, &quot;schema&quot; : &quot;https://github.com/citation-style-language/schema/raw/master/csl-citation.json&quot; }<span style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-GB">(Guillow, Lu, &amp; Grzebieta, 2001)</span><!--[if supportFields]><span lang=EN-GB style='mso-bidi-font-size:10.0pt'><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-GB"> using ultimate tensile stress as flow stress. Meanwhile for square tubes, test result agrees better with the analytical model by Abramowicz and Jones </span><!--[if supportFields]><span lang=EN-GB style='mso-bidi-font-size:10.0pt'><span style='mso-element:field-begin; mso-field-lock:yes'></span>ADDIN CSL_CITATION { &quot;citationItems&quot; : [ { &quot;id&quot; : &quot;ITEM-1&quot;, &quot;itemData&quot; : { &quot;DOI&quot; : &quot;http://dx.doi.org/10.1016/0734-743X(84)90010-1&quot;, &quot;abstract&quot; : &quot;A series of axial crushing tests on steel circular cylindrical shells loaded either statically or dynamically is reported and compared with various theoretical predictions and e/R0irical relations. A modified version of Alexander's theoretical analysis for axis!mmetric, or concertina, deformations gives good a~t with the experimental results when the effective crushing distance is considered and provided that the influence of material strain rate sensitivity is retained in the dynamic crushing case.&quot;, &quot;author&quot; : [ { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Abramowicz&quot;, &quot;given&quot; : &quot;W.&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; }, { &quot;dropping-particle&quot; : &quot;&quot;, &quot;family&quot; : &quot;Jones&quot;, &quot;given&quot; : &quot;N.&quot;, &quot;non-dropping-particle&quot; : &quot;&quot;, &quot;parse-names&quot; : false, &quot;suffix&quot; : &quot;&quot; } ], &quot;container-title&quot; : &quot;International Journal of Impact Engineering&quot;, &quot;id&quot; : &quot;ITEM-1&quot;, &quot;issue&quot; : &quot;3&quot;, &quot;issued&quot; : { &quot;date-parts&quot; : [ [ &quot;1984&quot; ] ] }, &quot;page&quot; : &quot;263-281&quot;, &quot;title&quot; : &quot;Dynamic axial crushing of circular tubes&quot;, &quot;type&quot; : &quot;article-journal&quot;, &quot;volume&quot; : &quot;2&quot; }, &quot;uris&quot; : [ &quot;http://www.mendeley.com/documents/?uuid=1a4a38b1-3c84-4481-9d9c-1bffd0888756&quot; ] } ], &quot;mendeley&quot; : { &quot;formattedCitation&quot; : &quot;(Abramowicz &amp; Jones, 1984a)&quot;, &quot;plainTextFormattedCitation&quot; : &quot;(Abramowicz &amp; Jones, 1984a)&quot;, &quot;previouslyFormattedCitation&quot; : &quot;(Abramowicz &amp; Jones, 1984a)&quot; }, &quot;properties&quot; : { &quot;noteIndex&quot; : 0 }, &quot;schema&quot; : &quot;https://github.com/citation-style-language/schema/raw/master/csl-citation.json&quot; }<span style='mso-element:field-separator'></span></span><![endif]--><span lang="EN-GB">(Abramowicz &amp; Jones, 1984a)</span><!--[if supportFields]><span lang=EN-GB style='mso-bidi-font-size:10.0pt'><span style='mso-element:field-end'></span></span><![endif]--><span lang="EN-GB"> using flow stress as the mean stress between yield stress and ultimate tensile stress.</span></p>