{"id":156531,"date":"2023-08-31T14:08:43","date_gmt":"2023-08-31T08:38:43","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=156531"},"modified":"2023-08-31T14:08:44","modified_gmt":"2023-08-31T08:38:44","slug":"a-plane-strain-compression-forging-of-a-block-is-shown-in-the-figure-the-strain-in-the-z-direction-is-zero","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/a-plane-strain-compression-forging-of-a-block-is-shown-in-the-figure-the-strain-in-the-z-direction-is-zero\/","title":{"rendered":"A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero"},"content":{"rendered":"\n<p>Q. A plane-strain compression (forging) of a block is shown in the figure. The strain in the <em>z<\/em>-direction is zero. The yield strength (<em>Sy<\/em>) in uniaxial tension\/compression of the material of the block is 300 MPa and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where s<em>x\u00a0<\/em>= 40 MPa (compressive) and t<em>xy <\/em>= 0, the stress component s\u00a0<em>y \u00a0<\/em>is<\/p>\n\n\n\n<figure class=\"wp-block-image aligncenter size-full\"><img decoding=\"async\" width=\"564\" height=\"302\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-666.png\" alt=\"\" class=\"wp-image-156532\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-666.png 564w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-666-300x161.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/figure>\n\n\n\n<p>Ans: 340 MPa (compressive)<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>According to Tresca&#8217;s theory<\/p>\n\n\n\n<p>\u03c3x+P=2K<\/p>\n\n\n\n<p>where,K=\u03c30\/2=flow shear stress<\/p>\n\n\n\n<p>=\u00a0300\/2=150MPa<\/p>\n\n\n\n<p>and&nbsp;\u03c3x=\u221240MPa<\/p>\n\n\n\n<p>Now,&nbsp;\u03c3x+P=2K<\/p>\n\n\n\n<p>=\u221240+P=2\u00d7150<\/p>\n\n\n\n<p>or P = 340 MPa<\/p>\n\n\n\n<p>P is pressure. If P = 340 MPa, stress&nbsp;(\u03c3y)&nbsp;will be &#8211; 340 MPa. i.e. 340 MPa (compressive)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero. The yield strength (Sy) in uniaxial tension\/compression of the material of the block is 300 MPa and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":156534,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-156531","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156531","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=156531"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156531\/revisions"}],"predecessor-version":[{"id":156535,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/156531\/revisions\/156535"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/156534"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=156531"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=156531"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=156531"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}