Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (2024)

Table of Contents
What is Strain? Types of Strain Stress-Strain Curve Explaining Stress-Strain Graph Hooke’s Law Elastic Moduli of Materials Frequently Asked Questions – FAQs What does the stress-strain curve show? What is the use of the stress-strain diagram? What is the relation between stress and strain? What is the yield point in stress-strain graph? How to make a stress-strain curve? Leave a Comment

The external force per unit area of the material resulting in the stretch of the material is known as tensile stress.

Compressive Stress

Compressive stress is the force that is responsible for the deformation of the material, such that the volume of the material reduces.

Read More: Compressive Stress

What is Strain?

Strain is the amount of deformation experienced by the body in the direction of force applied, divided by the initial dimensions of the body.

The following equation gives the relation for deformation in terms of the length of a solid:

\(\begin{array}{l}\epsilon = \frac{\delta l}{L}\end{array} \)

where ε is the strain due to the stress applied, δl is the change in length and L is the original length of the material.

The strain is a dimensionless quantity as it just defines the relative change in shape.

Types of Strain

Strain experienced by a body can be of two types depending on stress application as follows:

Tensile Strain

The deformation or elongation of a solid body due to applying a tensile force or stress is known as Tensile strain. In other words, tensile strain is produced when a body increases in length as applied forces try to stretch it.

Compressive Strain

Compressive strain is the deformation in a solid due to the application of compressive stress. In other words, compressive strain is produced when a body decreases in length when equal and opposite forces try to compress it.

Stress-Strain Curve

When we study solids and their mechanical properties, information regarding their elastic properties is most important. We can learn about the elastic properties of materials by studying the stress-strain relationships, under different loads, in these materials.

The material’s stress-strain curve gives its stress-strain relationship. In a stress-strain curve, the stress and its corresponding strain values are plotted. An example of a stress-strain curve is given below.

Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (1)

Explaining Stress-Strain Graph

The different regions in the stress-strain diagram are:

(i) Proportional Limit

It is the region in the stress-strain curve that obeys Hooke’s Law. In this limit, the stress-strain ratio gives us a proportionality constant known as Young’s modulus. The point OA in the graph represents the proportional limit.

(ii) Elastic Limit

It is the point in the graph up to which the material returns to its original position when the load acting on it is completely removed. Beyond this limit, the material doesn’t return to its original position, and a plastic deformation starts to appear in it.

(iii) Yield Point

The yield point is defined as the point at which the material starts to deform plastically. After the yield point is passed, permanent plastic deformation occurs. There are two yield points (i) upper yield point (ii) lower yield point.

(iv) Ultimate Stress Point

It is a point that represents the maximum stress that a material can endure before failure. Beyond this point, failure occurs.

(v) Fracture or Breaking Point

It is the point in the stress-strain curve at which the failure of the material takes place.

Hooke’s Law

In the 19th-century, while studying springs and elasticity, English scientist Robert Hooke noticed that many materials exhibited a similar property when the stress-strain relationship was studied. There was a linear region where the force required to stretch the material was proportional to the extension of the material, known as Hooke’s Law.

Hooke’s Law states that the strain of the material is proportional to the applied stress within the elastic limit of that material.

Mathematically, Hooke’s law is commonly expressed as:

F = –k.x

Where F is the force, x is the extension in length, and k is the constant of proportionality known as the spring constant in N/m.

Read More: Hooke’s Law

See the video below to learn about the stress-strain curve and Hooke’s law.

Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (2)

Elastic Moduli of Materials

The following table lists Young’s modulus, shear modulus and bulk modulus for common materials.

MaterialYoung’s modulus (E) in GPaShear modulus (G) in GPaBulk modulus (K) in GPa
Glass552337
Steel20084160
Iron9170100
Lead165.67.7
Aluminium702470

Note: GPa is gigapascal and 1 GPa = 1,00,00,00,000 Pa.

Related Reading
  • Poisson’s ratio
  • Young’s Modulus
  • Yield Strength
  • Plastic Deformation

Frequently Asked Questions – FAQs

Q1

What does the stress-strain curve show?

A stress-strain curve is a graphical way to show the reaction of a material when a load is applied. It shows a comparison between stress and strain.

Q2

What is the use of the stress-strain diagram?

The stress-strain diagram provides a graphical measurement of the strength and elasticity of the material. Also, the behaviour of the materials can be studied with the help of the stress-strain diagram, which makes it easy to understand the application of these materials.

Q3

What is the relation between stress and strain?

The relation between stress and strain is that they are directly proportional to each other up to an elastic limit. Hooke’s law explains the relationship between stress and strain. According to Hooke’s law, the strain in a solid is proportional to the applied stress and this should be within the elastic limit of that solid.

Q4

What is the yield point in stress-strain graph?

Yield point is defined as the point at which the material starts to deform plastically. After the yield point is passed, permanent plastic deformation occurs.

Q5

How to make a stress-strain curve?

The stress-strain curve is obtained by gradually applying load to a test coupon and measuring the deformation, from which the stress and strain can be determined.

See Also
Stress Strain Curve – Relationship, Diagram and Explanation - Mechanical Booster1.4: Stress-Strain CurvesStress vs strain curve (video) | Khan AcademyWhat is a Stress-Strain Curve? | Documentation | SimScale

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See Also
Stress-Strain Curve | How to Read the Graph?
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Comments

Leave a Comment

  1. Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (5)
    Lupho Mshumi July 16, 2020 at 3:54 am

    Thank you. It is clear, simple and easy to understand

    Reply

  2. Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (6)
    Girish harihar October 19, 2020 at 5:13 pm

    Strees and strain difference

    Reply

  • Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (7)
    sushmitha October 19, 2020 at 7:50 pm

    Learn about the difference between stress and strain here.

    Reply

Stress and Strain - Definition, Stress-Strain Curve, Hooke’s Law, SI Units (8)

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")}}):CS_UTILITIES.addToastMessage(0,"Session Expired")}});var I=T.find("[data-otp-voice-call-cta]");I.on("click",function(){var e=jQuery(this),r=30;e.find("span").html(" "+r+"sec."),e.attr("disabled",!0),u.attr("disabled",!1).focus(),_=setInterval(function(){--r,r<=0?(clearInterval(_),e.find("span").html("Voice Call"),e.attr("disabled",!1)):e.find("span").html(" "+r+"sec.")},1e3)})}var MOBILE_OTP_VALIDATER={isPhoneNumberVerified:!1,isUserAlreadyExist:!1,mobileNumber:"",verifyToken:"",verifyReference:"",apis:{register:BCAS_API_BASE_URL+"api/acs/v1/register",sendOtp:COMMON_UTILS_ENDPOINT_KEY+"otp",pageInstanse:"ask-question-popup",verifyOtp:COMMON_UTILS_ENDPOINT_KEY+"otp-verify",bcasSendOtp:BCAS_API_BASE_URL+"api/acs/v2/send-otp",bcasVerifyOtp:BCAS_API_BASE_URL+"api/acs/v2/verify-otp",voiceOtp:BCAS_API_BASE_URL+"api/acs/voice"},storageSessionId:""};

')))}):d.click(function(e){e.preventDefault();var a=USER_DETAILS_INPUT_VALIDATORS.phoneValidation(t)&&USER_DETAILS_INPUT_VALIDATORS.nameValiadation(r)&&USER_DETAILS_INPUT_VALIDATORS.emailValidation(i)&&USER_DETAILS_INPUT_VALIDATORS.requiredValidation(o,"","Comment")&&USER_DETAILS_INPUT_VALIDATORS.cityValidation(n,"","City")&&USER_DETAILS_INPUT_VALIDATORS.requiredValidation(s,"","Grade");if(a&&MOBILE_OTP_VALIDATER.isPhoneNumberVerified){jQuery(".cb-error-msg, .cb-success-msg").remove(),jQuery(d).attr("disabled",!0).text("Posting..."),DEFAULT_USER_DETAILS.isUserAlreadyLoggedIn=!0,DEFAULT_USER_DETAILS.isMobileAlreadyVerified=!0,MOBILE_OTP_VALIDATER.verifyToken?DEFAULT_USER_DETAILS.authorization=MOBILE_OTP_VALIDATER.verifyToken:(userFromStorage=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),authToken=userFromStorage.authorization,DEFAULT_USER_DETAILS.authorization=authToken),DEFAULT_USER_DETAILS.verifyKey||(userFromStorage=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),DEFAULT_USER_DETAILS.verifyKey=userFromStorage.verifyKey),void 0===SESSION_ID&&(DEFAULT_USER_DETAILS.sessionId=generateRandomID()),void 0===SESSION_ID_SECONDARY&&(DEFAULT_USER_DETAILS.sessionIdSecondary=generateRandomID());var l={first_name:r.val(),mobile_number:t.val(),email_address:i.val(),category_type:"COMMENT",session_id:DEFAULT_USER_DETAILS.sessionId,session_id_secondary:DEFAULT_USER_DETAILS.sessionIdSecondary,grade:s.val(),city:n.val(),authorization:DEFAULT_USER_DETAILS.authorization,currentUrl:C_URL,Website_URL:C_URL,Platform:void 0!==navigator.isMobile?navigator.isMobile?"website_mobile":"website_desktop":"",Lead_Magnet_Type:"LEAVE_A_COMMENT_FORM",Device_Details:void 0!==navigator.detectDeviceAgent?navigator.detectDeviceAgent:"",Device_UserAgent:void 0!==navigator.userAgent?navigator.userAgent:""},m=author_submit_form=email_submit_form=captcha_submit_form=!1;u.find('button[name="submit"]').attr("disabled","disabled").val("Posting...").addClass("post-class"),u.find('textarea[name="comment"]').removeClass("cb-error");var _=u.find('textarea[name="comment"]').val().trim(),S=_.replace(/(<([^>]+)>)/gi,"_HTML_").trim(),A=S.split(" ").join("\n");A=A.replace(/^\s*(\[\s*url\s*=\s*)?(https?:\/\/)?(www\.|\S+?\.)(\S+?\.)?\S+\s*$\s*/gm,"_URL_").trim(),""===_||null==_?u.find('textarea[name="comment"]').after('Please enter comment.').addClass("cb-error"):""===S||-1!==S.indexOf("_HTML_")?u.find('textarea[name="comment"]').after('HTML tags are not allowed for comment.').addClass("cb-error"):""===A||-1!==A.indexOf("_URL_")?u.find('textarea[name="comment"]').after('Any external links or urls are not allowed.').addClass("cb-error"):m=!0;var E={},p=jQuery("#data-comment-form"),v=p.serializeArray();if(jQuery.each(v,function(e,a){E[a.name]=a.value,"_wp_unfiltered_html_comment"===a.name&&null!==a.value&&(c=!0)}),!1===c)if(u.find('input[name="author"]').removeClass("cb-error"),u.find('input[name="email"]').removeClass("cb-error"),0!==u.find('textarea[name="g-recaptcha-response"]').length){var I=u.find('textarea[name="g-recaptcha-response"]').val().trim();""===I||null==I?u.find(".g-recaptcha").append('Please check the captcha form.'):captcha_submit_form=!0}else captcha_submit_form=!0;else author_submit_form=!0,email_submit_form=!0,captcha_submit_form=!0;m&&captcha_submit_form?(MOBILE_OTP_VALIDATER.verifyToken?E.authorization=MOBILE_OTP_VALIDATER.verifyToken:(userFromStorage=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),authToken=userFromStorage.authorization,E.authorization=authToken),E.comment=S,E.author=r.val(),E.email=i.val(),E.mobileNumber=l.mobile_number,delete E.city,delete E.grade,E.ajax_comment_request=1,jQuery.post(BASE_URL+"wp-comments-post.php",E,function(e){if(u.find('button[name="submit"]').attr("disabled",!1).val("Post Comment").removeClass("post-class"),null!=e){var a=JSON.parse(e);"success"===a.status&&a.response?(c?addGAEvent(USER_DETAILS_CONFIG.isUserAlreadyExist,"created Successfully"):(o.val(""),addGAEvent(USER_DETAILS_CONFIG.isUserAlreadyExist,"created Successfully"),0!==u.find('textarea[name="g-recaptcha-response"]').length&&grecaptcha.reset(),jQuery(d).attr("disabled",!1).text("Post Comment"),jQuery("#cancel-comment-reply-link").click(),jQuery(".form-submit").after('Thanks! Your comment has been submitted successfully. It will take some time to appear on the page.')),r.attr("disabled",!1).parent().removeClass("hidden"),i.attr("disabled",!1).parent().removeClass("hidden"),s.attr("disabled",!1).parent().removeClass("hidden"),n.attr("disabled",!1).parent().removeClass("hidden"),c||jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userCreateUpdateUrl,data:l,success:function(e){setStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE",JSON.stringify(DEFAULT_USER_DETAILS)),USER_DETAILS_CONFIG.isUserAlreadyExist=!0},error:function(e){console.log(e)}})):"invalid"===a.status&&a.response?(jQuery(d).text("Post Comment"),jQuery(".form-submit").after('Invalid Comment or User posted too many Comments')):"failed"===a.status&&a.response?(jQuery(d).text("Post Comment"),jQuery(".form-submit").after('Something went wrong, please refresh the page and try again')):(jQuery(d).attr("disabled",!1).text("Post Comment"),jQuery(".form-submit").after('Invalid Comment or User posted too many Comments'))}else jQuery(d).attr("disabled",!1).text("Post Comment"),jQuery(".form-submit").after('Something went wrong. Please try again after sometime.'),addGAEvent(USER_DETAILS_CONFIG.isUserAlreadyExist,"creation Failed")})):u.find('button[name="submit"]').attr("disabled",!1).val("Post Comment").removeClass("post-class")}else USER_DETAILS_INPUT_VALIDATORS.phoneValidation(t),USER_DETAILS_INPUT_VALIDATORS.nameValiadation(r),USER_DETAILS_INPUT_VALIDATORS.requiredValidation(o,"","Comment "),USER_DETAILS_INPUT_VALIDATORS.cityValidation(n,"","City"),USER_DETAILS_INPUT_VALIDATORS.requiredValidation(s,"","Grade"),USER_DETAILS_INPUT_VALIDATORS.emailValidation(i),USER_DETAILS_INPUT_VALIDATORS.phoneValidation(t)&&!MOBILE_OTP_VALIDATER.isPhoneNumberVerified&&(a=!1,r.removeClass("input-valid").addClass("input-error"),r.siblings(".input-error-msg").remove(),t.removeClass("input-valid").addClass("input-error"),t.siblings(".input-error-msg").remove(),t.after('

Validate your Mobile Number

'))})),getInputAccordingSessionID(e,t,l,m,r,i,n,s),t.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.phoneValidation(this)}),o.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.requiredValidation(this,"","Comment ")}),r.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.nameValiadation(this)}),i.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.emailValidation(this)}),s.on("input",function(){USER_DETAILS_INPUT_VALIDATORS.requiredValidation(this,"","Grade")}),n.on("input",function(){this.isValidInput=USER_DETAILS_INPUT_VALIDATORS.cityValidation,this.requiredName="City";var e=jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(e,"","City")}),n.on("change",function(){this.isValidInput=USER_DETAILS_INPUT_VALIDATORS.cityValidation,this.requiredName="City";var e=jQuery(this);USER_DETAILS_INPUT_VALIDATORS.cityValidation(e,"","City")})}}function addGAEvent(e,a){e?GA_FLAG&&ga("send","event","Post Comment Successful","Post Comment activity "+a+" By Existed User","URL: "+C_URL):GA_FLAG&&ga("send","event","Post Comment Successful","Post Comment activity "+a+" By New User","URL: "+C_URL)}function getInputAccordingSessionID(e,a,t,r,i,s,n,o){var d,l;if(null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")&&(d=JSON.parse(getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")),l=d.sessionId,sessionIDSec=d.sessionIdSecondary,void 0!==l&&"undefined"!=typeof sessionIDSec)){var m={session_id:l,session_id_secondary:sessionIDSec};jQuery.ajax({type:"POST",url:USER_DETAILS_CONFIG.apis.userChecBySessionIDUrl,data:m,success:function(e){e.success&&(a.val(e.data.mobile).attr("disabled",!0),t.addClass("hidden"),r.removeClass("hidden"),i.val(e.data.name).attr("disabled",!1).parent().removeClass("hidden"),s.val(e.data.email).attr("disabled",!1).parent().removeClass("hidden"),n.val(e.data.city).attr("disabled",!1).parent().removeClass("hidden"),o.val(e.data.grade).attr("disabled",!1).parent().removeClass("hidden"),MOBILE_OTP_VALIDATER.isPhoneNumberVerified=d.isMobileAlreadyVerified,USER_DETAILS_CONFIG.isUserAlreadyExist=!0,USER_DETAILS_CONFIG.userDetails=e.data)},error:function(e){console.log(e)}})}}var SESSION_ID,SESSION_ID_SECONDARY,DEFAULT_USER_DETAILS={author:"",email:"",mobile:"",isUserAlreadyLoggedIn:!1,isMobileAlreadyVerified:!1,sessionId:"",sessionIdSecondary:"",authorization:"",verifyKey:""},USER_DETAILS_CONFIG={isUserAlreadyExist:!1,apis:{userChecBySessionIDUrl:BASE_URL+"wp-json/spidy/v1/get_user_by_session_id_api/",userCheckUrl:BASE_URL+"wp-json/spidy/v1/user_check_api/?wp-json_allow",userCreateUpdateUrl:BASE_URL+"wp-json/spidy/v1/user_create_update_api/?wp-json_allow",city:{url:BCAP_API_BASE_URL+"api/geo_dimensions/india_state_city_list/?limit="+INDIA_STATE_CITY_LIST_LIMIT_VAL,method:"GET"}},userDetails:""},USER_DETAILS_INPUT_VALIDATORS={getParameterByName:function(e,a){a=a?"?"+a:window.location.search;var t=new RegExp("[?&]"+e.replace(/\[/g,"\\[").replace(/\]/g,"\\]")+"(?:=([^]*))?(?:[]|$)").exec(a);return t?t[1]?decodeURIComponent(t[1].replace(/\+/g," ")):"":null},requiredValidation:function(e,a,t){var r=jQuery(e),i=r.val(),s="";return r.siblings(".input-error-msg").remove(),i&&null!==i||(s=t+" is required."),s?(r.addClass("input-error").removeClass("input-valid"),r.after('

'+s+"

"),!1):(r.removeClass("input-error"),r.addClass("input-valid"),!0)},emailValidation:function(e,a){var t=jQuery(e),r=t.val(),i="",s=/^(([^<>()[\]\\.,;:\s@\"]+(\.[^<>()[\]\\.,;:\s@\"]+)*)|(\".+\"))@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\])|(([a-zA-Z\-0-9]+\.)+[a-zA-Z]{2,13}))$/;return t.siblings(".input-error-msg").remove(),r&&null!==r?r.match(s)||(i="Email-id is not valid."):i="Email-id is required.",i?(t.addClass("input-error").removeClass("input-valid"),t.after('

'+i+"

"),!1):(t.removeClass("input-error"),t.addClass("input-valid"),!0)},nameValiadation:function(e,a,t){var r=jQuery(e),i=r.val(),s=t||"Name",n="",o=/^[a-zA-Z][a-zA-Z\-\ \.]{2,}$/i;return r.siblings(".input-error-msg").remove(),n=i&&null!==i?i.length<=2?"Name should be minimum 3 characters.":i.match(o)?"":"Accepts alphabets only.":s+" is required.",n?(r.addClass("input-error").removeClass("input-valid"),r.after('

'+n+"

"),!1):(r.removeClass("input-error"),r.addClass("input-valid"),!0)},phoneValidation:function(e,a){var t=jQuery(e),r=t.val(),i="",s=/^\d{10}$/,n=/^\d{1,10}$/;if(t.siblings(".input-error-msg").remove(),r&&null!==r)if(r.match(n))r.match(s)||(i="Mobile No. should be 10 digits.");else{let e=t.val().replace(/[^0-9]+/g,"");t.val(e),i=t.val()?"Mobile No. should be 10 digits.":"Mobile No. is required."}else i="Mobile No. is required.";return i?(t.addClass("input-error").removeClass("input-valid"),t.after('

'+i+"

"),!1):(t.removeClass("input-error"),t.addClass("input-valid"),!0)},ajaxCall:function(e,a,t,r){jQuery.ajax({type:e,url:a,crossDomain:!0,data:t,headers:{"content-type":"application/x-www-form-urlencoded"},success:function(e){r&&r(e)},error:function(e){r&&r(e)}})},cities:[],cityAutoSuggestions:function(e){var a;USER_DETAILS_INPUT_VALIDATORS.ajaxCall(USER_DETAILS_CONFIG.apis.city.method,USER_DETAILS_CONFIG.apis.city.url,"",function(e){e.results.length&&(a=e.results,USER_DETAILS_INPUT_VALIDATORS.cities=e.results)});var t=jQuery("["+e+"]"),r=t.find("input");r.on("input",function(){0;var e=jQuery(this).val().toLowerCase(),i="";if(t.find("ul").remove(),e.length>=1){var s=jQuery.grep(a,function(a,t){return 0===a.city.toLowerCase().indexOf(e)});s.length&&(s.every(function(a,t){return i+='

  • '+a.city.toLowerCase().replace(e,""+e+"")+"

    • ",6!==t}),t.append("

      "+i+"

    "))}t.find("ul>li>a").on("click",function(e){e.stopPropagation(),r.val(jQuery(this).text()),t.find("ul").remove(),0,r[0].isValidInput(r)})}),jQuery("body").on("click",function(){t.find("ul").remove(),0})},cityValidation:function(e,a,t){if(USER_DETAILS_INPUT_VALIDATORS.requiredValidation(e,a,t)){if(!USER_DETAILS_INPUT_VALIDATORS.cities.length)return!0;if(USER_DETAILS_INPUT_VALIDATORS.cities.filter(function(a){return a.city.toLocaleLowerCase()==e.val()}).length)return e.siblings(".input-error-msg").remove(),e.removeClass("input-error"),e.addClass("input-valid"),!0;e.addClass("input-error").removeClass("input-valid"),e.after('

    Should be selected from the list

    ')}return!1}};(function(){if(jQuery("#data-comment-form").length>0){commentForm("COMMENT");var e=jQuery("[data-name-field]"),a=jQuery("[data-email-field]"),t=jQuery("[data-grade-fg]"),r=jQuery("[data-city-fg]");e.length>0&&a.length>0&&phoneNumberValidation("#data-comment-form",e,a,t,r,"COMMENT"),USER_DETAILS_INPUT_VALIDATORS.cityAutoSuggestions("data-city-auto-suggestions-comment")}})(),window.onbeforeunload=function(){null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE")&&clearLocalStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE"),null!==getStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE_expiresIn")&&clearLocalStorage("DEFAULT_COMMENT_BOX_LOCALSTORAGE_expiresIn")};

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