{"id":162,"date":"2013-08-21T11:14:59","date_gmt":"2013-08-21T16:14:59","guid":{"rendered":"https:\/\/my.vanderbilt.edu\/cpml\/?page_id=162"},"modified":"2013-08-21T11:23:59","modified_gmt":"2013-08-21T16:23:59","slug":"mixed-mode-fracture-in-composites","status":"publish","type":"page","link":"https:\/\/my.vanderbilt.edu\/cpml\/mixed-mode-fracture-in-composites\/","title":{"rendered":"Mixed mode fracture in composites"},"content":{"rendered":"<p>A discrete damage zone model aimed at simulating fracture initiation and  propagation within the framework of the finite element method is  proposed. The approach is related to the discrete cohesive zone models  where cohesive laws (also known as traction-separation laws) are  introduced through a set of nonlinear springs attached to the finite  element nodes where fracture is assumed to occur. In the proposed  approach, rather than employing specific cohesive laws at the element  edges, we employ damage laws to prescribe both interface spring  softening and bulk material stiffness degradation to study crack  propagation. For a homogeneous isotropic material the same damage law is  assumed to hold in both the continuum and the interface elements.  Accordingly, three scalar damage variables are introduced, one to model  the damage of the continuum and the other two to model the degradation  of the discrete spring elements. The parameters of the assumed damage  law are calculated from the principles of linear elastic fracture  mechanics. The proposed discrete damage zone model (DDZM) is implemented  in Abaqus via the user defined element (UEL) subroutine. Numerical  results for single-mode and mixed-mode delamination are presented. The  results are in good agreement with those obtained from the virtual crack  closure technique (VCCT) and available analytical solutions, thus,  illustrating the validity of this approach. Finally, the suitability of  the method for studying fracture in fiber-matrix composites involving  fiber debonding and matrix cracking is illustrated.<a href=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/754\/2013\/08\/cpml-research-5.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-large wp-image-73\" src=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/754\/2013\/08\/cpml-research-5-650x233.jpg\" alt=\"\" width=\"650\" height=\"233\" srcset=\"https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/754\/2013\/08\/cpml-research-5-650x233.jpg 650w, https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/754\/2013\/08\/cpml-research-5-300x107.jpg 300w, https:\/\/cdn.vanderbilt.edu\/t2-my\/my-prd\/wp-content\/uploads\/sites\/754\/2013\/08\/cpml-research-5.jpg 1112w\" sizes=\"auto, (max-width: 650px) 100vw, 650px\" \/><\/a>Fracture in fiber-matrix composites involving fiber debonding as well as matrix cracking. Figure <strong>a<\/strong> shows the geometry and dimensions of the square unit cell and the zoom of the discrete elements near fiber-matrix interface. Figure <strong>b<\/strong> shows the numerical result wherein the ultimate failure of the unit cell occurs through a combination of breaking of spring elements and continuum damage in finite elements.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>A discrete damage zone model aimed at simulating fracture initiation and propagation within the framework of the finite element method is proposed. The approach is related to the discrete cohesive zone models where cohesive laws (also known as traction-separation laws) are introduced through a set of nonlinear springs attached to the finite element nodes where&#8230;<\/p>\n","protected":false},"author":1985,"featured_media":73,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[5],"class_list":["post-162","page","type-page","status-publish","has-post-thumbnail","hentry","tag-featured"],"_links":{"self":[{"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/pages\/162","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/users\/1985"}],"replies":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/comments?post=162"}],"version-history":[{"count":4,"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/pages\/162\/revisions"}],"predecessor-version":[{"id":182,"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/pages\/162\/revisions\/182"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/media\/73"}],"wp:attachment":[{"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/media?parent=162"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/my.vanderbilt.edu\/cpml\/wp-json\/wp\/v2\/tags?post=162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}