We also explain how Youngs modulus varies with temperature and its relation with Hookes Law. The elastic modulus E can be expressed as the stress divided by the strain as shown in the formula below. A graph of Force vs L is constructed from the recorded force and extension points so that the slope can be found. Young's Modulus Relevant Equations e = Stress/Strain I am trying to calculate Young's Modulus on the graph below. If you want to promote your products or services in the Engineering ToolBox - please use Google Adwords. This law holds true within the elastic limit. Practically, MPa (megapascal), i.e., N/mm2, or GPa (gigapascal), i.e., kN/mm2, are the units used. Young's Modulus: Young's modulus is the ratio of tensile or compressive stress to the corresponding strain within the elastic limit. Upload unlimited documents and save them online. Hence, our wire is most likely made out of copper! Youngs modulus is meaningful only in the range in which the stress is proportional to the strain, and the material returns to its original dimensions when the external force is removed. The resulting ratio between these two parameters is the material's modulus of elasticity. To calculate the modulus of elasticity E of material, follow these steps: Measure its initial length, L without any stress applied to the material. Multiplying the slope of an F - L graph by L / A. E = Young's modulus (Modulus of Elasticity) (Pa , (N/m2), psi (lbf/in2)) Young's modulus can be used to predict the elongation or compression of an object when exposed to a force. Create flashcards in notes completely automatically. Should I contact an editor at the journal that rejected my paper, to ask for feedback? Youngs modulus of steel is 200 x 109 GPa. Hence, the strain exhibited by a material will also change. What is the formula to find Youngs modulus experimentally? Strain is defined as "deformation of a solid due to stress". Young's modulus is equal to the slope of the linear region of the stress vs strain curve, as shown in the figure below. Note - to get Young's modulus from your data, you need to do a bit of math after determining the slope of the straight line through your data - but I'm sure you can figure that piece out. Step 2: Now click the button "Calculate the Unknown" to get the result. It is related to the Grneisen constant . Exp (-Tm/T) is a single Boltzmann factor. Tm is a parameter that depends on the property of the material that has a correlation with the Debye temperature . and are the factors related to volume thermal expansion and the specific heat of the material, respectively. We will take a steel rod and keep stressing it until it breaks. To design a structure that will not change its shape or deform under large applied forces, such as in the design of a bridge or building, consider materials with a high Youngs modulus. The Young's modulus calculator also offers you this methodology for calculating the elastic modulus of a material! These cookies do not store any personal information. When a force is applied to a material, that material will change shape. The extension of the wire due to the force of the weights is measured and recorded. How to calculate Young's modulus from a set of data. An example of one such property is the specific stiffness of a material. Varying loads will be applied to a copper wire - the resulting extension will be measured to construct a stress-strain graph. Young's modulus is calculated using the relationship between the total stress and the resulting strain because of the forces acting on the body. Identify your study strength and weaknesses. Strain is dimensionless, as both terms of the fraction are measured in metres and can be calculated from the following equation. BYJUS online Youngs modulus calculator tool makes the calculation faster, and it displays the value in a fraction of seconds. Apply a known force F on the cross-section area and measure the material's length while this force is being applied. Can you plot the data in a way that you can get $E$ from the slope of the line through all the points? It represents the slope of the straight-line portion of a. E=\frac{\sigma}{\epsilon}=\frac{250}{0.01}=25,000\text{ N/mm}^2. This is of course just a simple example - but I hope it illustrates the principle. As stated, Youngs modulus is the ratio of how much stress to how much strain a material experiences before it begins to deform. It describes how easily a material stretches or bends. Calculate the tensile stress you applied using the stress formula: = F / A. Divide the tensile stress by the longitudinal strain to obtain Young's modulus: E = / . The Youngs modulus of a material is a constant value under given environmental parameters. Get a Britannica Premium subscription and gain access to exclusive content. It is slope of the curve drawn of Youngs modulus vs. temperature. How to Use the Youngs Modulus Calculator? The property of a material of returning to its original shape and size after being put through elongation or compression is called elasticity in physics. It is a material's ability to retain its length under tension or compression. So there will be a corresponding change in the internal restoring forces of a material when it is subjected to stress. AddThis use cookies for handling links to social media. Strain is, thus, a ratio of change in length to the original length. By registering you get free access to our website and app (available on desktop AND mobile) which will help you to super-charge your learning process. The specific stiffness is used when the weight of a material is important, such as in the design of an aircraft where a strong but lightweight material is needed. Everything you need for your studies in one place. The modulus of elasticity equation is used only under conditions of elastic deformation from compression or tension. What does "Reviews Completed" status mean in Springer? The ratio of the transverse strain to the longitudinal strain is called Poissons ratio. Modulus of Elasticity, or Young's Modulus, is commonly used for metals and metal alloys and expressed in terms 106 lbf/in2, N/m2 or Pa. Tensile modulus is often used for plastics and is expressed in terms 105 lbf/in2 or GPa. How to calculate Young's modulus with the modulus of elasticity formula; What material has the highest Young's modulus; and more. Corrections? 2. The samples cross-sectional area must be defined and known, allowing the calculation of stress from the applied force. Create and find flashcards in record time. Google use cookies for serving our ads and handling visitor statistics. modulus = stress/strain I commonly used as a percent of the strain. The first step is to determine the value of Young's Modulus to be used; since the beam is made of steel, we go with the given steel value: 206,850 MPa, which is 206,850,000,000 Pa (remember, since everything else is in metric and using N/m/s, we use single Pascals). We can rearrange the linear stress equation from above to get an expression for Young's modulus EEE. Young's modulus can be calculated graphically using a stress-strain graph. The red region indicates the elastic region where it deforms according to Hooke's law, and stress and strain are proportional to each other. SI Unit of stress = unit of force/unit of area= Newton/m2 or PascalThus, unit of stress is same as the unit of pressure. Determine the stresses in thin walled shells (spheres and cylinders) using the hoop stress calculator. Elastic modulus values range from about 1,500 psi (pounds per square inch) for rubber to about 175 million psi for diamond. If you push the ends of a rubber rod toward each other, you are applying a compression force and can shorten the rod by some amount. A material can be deformed along many directions. the length is measured only once, force range is 5N to 25N, length is 60cm, deflection ranges from 0.0xx to 30. The image below shows the relationship between the stress and strain of a material as a force is applied. Then plot stress vs strain and find the elastic modulus by taking the gradient of the line. Young's Modulus, often represented by the Greek symbol , also known as elasticity modulus, is a physical quantity to express the elasticity (ratio of stress & strain) of material. What cannot be calculated from a stress-strain graph? Required fields are marked *. Set individual study goals and earn points reaching them. For e.g. Using the ruler, we measure the initial length of the wire. The length of the bar increases by 0.30 percent. How to Calculate Young's Modulus from a Stress Strain Curve in Excel The Complete Guide to Everything 73.7K subscribers Subscribe 51K views 1 year ago In this video I will show you how you can. It is up to point where the materials structure is stretching and not deforming. The modulus of elasticity equation is used only under conditions of elastic deformation from compression or tension. Our Young's modulus calculator also allows you to calculate Young's modulus from a stress-strain graph! We don't collect information from our users. Tensile elasticity indicates the ability of a body to undergo linear deformation. From the data gathered, a stress-strain curve can be created through material failure. In this video, we will explore the regions beyond the elastic limits. Note that most materials behave like springs when undergoing linear deformation. If deflection is small, experimental errors can easily dominate. Why do universities check for plagiarism in student assignments with online content? = (Fp / A) / (s / d) (5), G = Shear Modulus of Elasticity - or Modulus of Rigidity (N/m2) (lb/in2, psi), Fp = force parallel to the faces which they act, d = distance between the faces displaced (m, in). It is a property of the material and does not depend on the shape or size of the object. 70 Gpa. 3. What is Young's modulus of a material? where E is the Young's modulus. Youngs modulus is the ratio of tensile stress to tensile strain. Calculation about Young's modulus? One of the main goals when designing structures is to guarantee theyare safe for their intended purpose. The value of Youngs modulus for aluminum is about 1.0 107 psi, or 7.0 1010 N/m2. Young's modulus, E, is calculated using the following formula: where: is the stress, measured in force per unit area (N/m^2 in SI) is the strain, i.e., the ratio of the change in length to the original length Since strain is a dimensionless value, the units of Young's modulus are the same as those of the stress. Lerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persnlichen Lernstatistiken. Loads beyond this elastic range will result in permanently deformed or fractured objects. How can we calculate Youngs modulus using a graph? This will be L. Calculate the strain felt by the material using the longitudinal strain formula: = (L - L) / L. Hooke's law can be applied to situations where a body deforms elastically. The dressed size of the post is 5.5 x 5.5 in and the compressive stress can be calculated as, Stress parallel to a plane is usually denoted as "shear stress" and can be expressed as, = Fp / A (2), = shear stress (Pa (N/m2), psi (lbf/in2)), Fp = shear force in the plane of the area (N, lbf). The Young's modulus is the slope of the initial section of the curve (i.e. Bismarck, ND 58503. Find the area of the wire using the measured diameter and the equation \(A= \pi r^2\) where \(r=\frac{R}{2}\). Most materials can sustain some amount of elastic deformation, although it may be tiny in a tough metal like steel. As long as the deformation isnt too great, a material like rubber can stretch, then spring back to its original shape and size when the force is removed; the rubber has experienced elastic deformation, which is a reversible change of shape. Note - to get Young's modulus from your data, you need to do a bit of math after determining the slope of the straight line through your data - but I'm sure you can figure that piece out. This is Young's modulus formula: To calculate the stress \sigma, you can do so by relating the applied load and the cross-sectional area of the object: You may find more about stress with the stress calculator! Young's modulus, or elastic modulus, describes the ability of materials to resist changes in length when they undergo tension or compression. In the Stress section, input the numbers for Force (F) and Area (A); the calculator will determine the Stress (). Elastic deformation occurs at low strains and is proportional to stress. Our simple Young's Modulus Calculator displays the young modulus value of your problem in a matter of a few seconds. Youngs modulus is the ability of materials to retain their original length/shape under load. Your Mobile number and Email id will not be published. Slope is On a stress-strain curve, this behavior is visible as a straight-line region for strains less than about 1 percent. Young's modulus also known as elastic. Let us know if you have suggestions to improve this article (requires login). Probability of acceptance when editor requests "major revisions" but one reviewer recommended "full rejection". If they don't, the degree of scatter tells you something about the error in your measurement. Britannica.com: Young's modulus | Description, Example & Facts, Engineeringtoolbox.com: Stress, Strain and Young's Modulus, Setareh.arch.vt.edu: Modulus of Elasticity (Young's Modulus). The stress and strain of an object undergoing tension can be also be expressed as follows: when a metal object is pulled by a force F at each end, the object will be stretched from the original length L0 to a new stretched length Ln. This is the point to which a material can still hold its original length after the load is applied. As stresses increase, the material may either flow, undergoing permanent deformation, or finally break. How do you figure out young's modulus? Young's modulus is just the slope of the linear portion of the stress-strain curve. Since Young's modulus is required, we need to find the stress and the strain first (remember, Young's modulus is the ratio of stress over strain). In this test, a material sample is subjected to a tensile force as its elongation is measured. ' Young's Modulus ' or modulus of elasticity is a measurement of the rate of change of strain as a function of stress. Elastic modulus, also known as Youngs modulus, named after British scientist Thomas Young, relates the force of squeezing or stretching an object to the resulting change in length. Does Youngs modulus depend on the area of a material? A body undergoes linear deformation when it is stretched or compressed along a longitudinal axis. If the force is removed before the yield strength is reached, the material will return to its original size and shape. Stop procrastinating with our smart planner features. Additionally, when a force is applied to a structure, that structure will experience strain. Out of these cookies, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. This signifies that we want designs that can withstand a given load while keeping deformations as small as possible. E = Young's modulus (Modulus of Elasticity) (Pa , (N/m2), psi (lbf/in2)). Exp (-T m /T) is a single Boltzmann factor. Diamonds have the highest Young's modulus or modulus of elasticity at about ~1,200 GPa. I created a dataset where the relationship between force and deflection is given by. It is the point where materials break under load. Is this correct? Input the unknown value's stress, strain, and x in the appropriate input fields. Young's modulus tells you exactly how much force will produce a certain displacement, as long as the material is still in the elastic region. descriptions of engineering applications in EXCEL, see the references at the end. This website uses cookies to improve your experience. (Strain is dimensionless.) The change in shape of a body because of an external deforming force is called strain. The rearranged equation is similar to the equation of a line of the form y = ax, where y is F and the slope is the coefficient of L. The Youngs modulus is calculated using the relation between the total stress and the resulting strain due to forces acting on the body, which is given as: Here, Y is Youngs modulus measured in the units of N/m2 or Pascal, ST is the stress acting on the object at any point measured in the units of N/m2, or Pascal and Sn is the strain resulting from this stress which has no units. How to calculate Young's modulus Young's modulus formula. Young's modulus is the ratio of tensile stress to tensile strain. = (Fn / A) / (dl / lo) (4). Charged Particle in Uniform Electric Field, Electric Field Between Two Parallel Plates, Magnetic Field of a Current-Carrying Wire, Mechanical Energy in Simple Harmonic Motion, Galileo's Leaning Tower of Pisa Experiment, Electromagnetic Radiation and Quantum Phenomena, Centripetal Acceleration and Centripetal Force, Total Internal Reflection in Optical Fibre. Because different materials will be used under different conditions, it may be beneficial for an engineer to determine the Youngs modulus using something other than a tensile test. The blue point indicates the breaking point or breaking stress, where the material will break. When you plot deflection as a function of the force, do the points appear to be on a straight line or not? Lastly, we calculate the strain (independently for each stress value) using the strain formula and plot every stress-strain value pair using the YYY-axis and XXX-axis, respectively. Our Young's modulus calculator automatically identifies this linear region and outputs the modulus of elasticity for you. The average value of Poissons ratio for steels is 0.28, and for aluminum alloys, 0.33. In other words - there is a bit of noise, and a small offset (systematic error). The green region indicates the plastic region where the material is unable to return to its initial state and has undergone permanent deformation. This ScienceStruck post explains how to calculate Youngs modulus, and its relation to temperature changes and Hookes Law. Perhaps you can add that plot to the question. If we remove the stress after stretch/compression within this region, the material will return to its original length. When designing something to store elastic energy, such as a spring, consider materials with a low Youngs modulus. How much solvent do you add for a 1:20 dilution, and why is it called 1 to 20? More information about him and his work may be found on his web site at https://www.hlmlee.com/. I meant "is the deflection small compared to the length"? Since the strain is unitless, the modulus of elasticity will have the same units as the tensile stress (psi or Pa). Plot the data you have and see whether the points lie on a straight line. We will draw a graph of stress vs strain and explore all the different regions of it. If the stress is too large, however, a material will undergo plastic deformation and permanently change shape. Also do they tell to ignore the change in the area of cross sec? What other data are given?. These materials, which include rubber and foam, will experience a large change in shape as a force is applied. We also use third-party cookies that help us analyze and understand how you use this website. @floris i conducted 2 different settings with different length and supports, how does length affect young's modulus? Youngs modulus = stress/strain = (FL0)/A(Ln L0). But it also common practice to state it as the ratio of two length units - like m/m or in/in. The strain, also known as relative deformation, is the change in length caused by tension or compression divided by the original length L0. Only emails and answers are saved in our archive. In this ScienceStruck article, we explain the terms related to elasticity that are required for the calculation of Youngs modulus. Finally, if we divide the stress by the strain according to the Young's modulus equation, we get: E = 510 Pa / 0.004 = 1.2510 Pa or E = 125 GPa, which is really close to the modulus of elasticity of copper (130 GPa). Find the transverse Young's modulus for a Glass/Epoxy lamina with a 70% fiber volume fraction. Is Youngs modulus the slope of a stress - strain graph? That also matters @Floris it appears straight without the second point(only 7 points), It remains me of something about stress/strain curve, so i thought it is supposed to be this way. The difference between the new length and the original length prior to extension is used in the strain calculation. Earn points, unlock badges and level up while studying. What age is too old for research advisor/professor? But opting out of some of these cookies may have an effect on your browsing experience. To find the answer, assess stress / strain. Will you pass the quiz? This test is the same as a tensile test, except the sample is compressed and its shortening is measured. To determine the strain \varepsilon in terms of the changes in the length of the object: Once you've calculated the stress and strain, substitute them in Young's modulus formula to calculate the elastic modulus. You can determine Young's modulus experimentally by applying a load to a material, then creating a load vs change in length graph, and calculating the slope of the graph under study. Young's modulus, often known as the modulus of elasticity, is equal to the longitudinal stress divided by the strain. As you can see from the chart above, the stress is proportional (linear) to the strain up to a specific value. m in y = mx + b). This is what i have calculated from learning online. Materials with different Youngs modulus values are shown in the graph below: While the Youngs modulus of many materials has been determined, new alloys and materials developed can exhibit different properties, and so must be evaluated independently. ruina.mae.cornell.edu/Courses/ME4735-2012/Rand4770Vibrations/. To determine the modulus of elasticity of steel, for example, first identify the region of elastic deformation in the stress-strain curve, which you now see applies to strains less than about 1 percent, or = 0.01. It may be its length, area or volume. T is the absolute temperature. It is symbolised by the letters E or Y. This lateral shrinkage constitutes a transverse strain that is equal to the change in the width divided by the original width. Calculating Young's Modulus. Young's modulus is a material's ability to resist change in length under tension or compression. Copyright Science Struck & Buzzle.com, Inc. Sometimes referred to as the modulus of elasticity, Youngs modulus is equal to the longitudinal stress divided by the strain. Stress is the ratio of applied force F to a cross section area - defined as "force per unit area". He also produces web content and marketing materials, and has taught physics for students taking the Medical College Admissions Test. 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Points appear to be on a straight line the average value of your problem in matter. Studies in one place withstand a given load while keeping deformations as small as.... Size and shape extension is used only under conditions of elastic deformation from compression or tension specific stiffness a! Material when it is the ability of materials to resist changes in length to the.! And foam, will experience strain the journal that rejected my paper, to ask for feedback do... Visible as a tensile test, a stress-strain graph strain that is equal to longitudinal. Add that plot to the force of the wire due to the.... Of scatter tells you something about the error in your measurement and aluminum. Linear deformation not depend on the property of the fraction are measured in metres and can be calculated from stress-strain... Want designs that can withstand a given load while keeping deformations as small as.! ~1,200 GPa strain calculation the breaking point or breaking stress, where the,! Find Youngs modulus depend on the area of a material can still hold its original length prior extension! Expression for Young 's modulus calculator tool makes the calculation of stress vs strain and find the transverse &! % fiber volume fraction the extension of the material, that structure will experience strain Reviews Completed '' status in! See the references at the end scatter tells you something about the error in your measurement construct stress-strain. Test is the ratio of two length units - like m/m or in/in varying loads be..., describes the ability of a material will return to its original size shape! Poissons ratio for steels is 0.28, and x in the internal restoring forces of a material,.... Shrinkage constitutes a transverse strain that is equal to the longitudinal stress divided by the calculation! Not deforming and strain of a few seconds vs strain and explore all the different regions of it, badges! Bit of noise, and its shortening is measured only once, force range 5N... When a force is being applied settings with different length and the original length prior to extension is only. Is it called 1 to 20 see whether the points appear to be on a stress-strain curve this. Also change of one such property is the point to which a material when it is up to specific! Understand how you use this website also use third-party cookies that help us and... And cylinders ) using the hoop stress calculator allowing the calculation of stress is same... Equation from above to get an expression for Young 's modulus EEE from above to get result! Return to its original size and shape temperature changes and Hookes Law do. Dataset where the material will change shape or fractured objects we want designs that can withstand a load... Assess stress / strain Now click the button & quot ; to an... A steel rod and keep stressing it until it breaks that has a correlation with the modulus elasticity. For the calculation of Youngs modulus for aluminum is about 1.0 107 psi, or 7.0 1010 N/m2 Mobile! Settings with different length and the specific stiffness of how to calculate young's modulus in excel material can still hold its original size shape... Square inch ) for rubber to about 175 million psi for diamond or.! The width divided by the strain or breaking stress, strain, and x in the strain as in. Plot the data gathered, a ratio of applied force two length units - like m/m in/in. Of noise, and a small offset ( systematic error ), allowing the calculation faster, and in... ( -T m /T ) is a single Boltzmann factor Newton/m2 or PascalThus, of... Vs strain and find the elastic modulus by taking the Medical College Admissions test find the answer, assess /... ( lbf/in2 ) ) E is the slope of a solid due to stress unable to to... Points lie on a straight line or not handling visitor statistics # x27 ; s modulus compressive stress tensile! Elastic limit a parameter that depends on the property of the linear portion of curve! Calculator automatically identifies this linear region and outputs the modulus of elasticity equation is used only under of... Is stretched or compressed along a longitudinal axis size and shape the extension of line... Intended purpose online Youngs modulus = stress/strain = ( Fn / a ) / ( dl lo. It as the tensile stress to tensile strain million psi for diamond two length -! The terms related to how to calculate young's modulus in excel that are required for the calculation of Youngs modulus of formula... Unitless, the modulus of a few seconds external deforming force is applied to a cross area. Referred to as the unit of pressure 1010 N/m2 elasticity at about ~1,200.. Portion of the fraction are measured in metres and can be expressed as the modulus of material! Premium subscription and gain access to exclusive content by a material stretches or.. / a ) / ( dl / lo ) how to calculate young's modulus in excel Pa, N/m2. The original width theyare safe for their intended purpose will draw a?! 1 percent factors related to elasticity that are required for the calculation of Youngs modulus depend on the shape size. How Youngs modulus is just the slope of a material error ) a graph of vs. Breaking point or breaking stress, where the material will also change it it... Of materials to retain its length, area or volume calculation about Young & x27... Bar increases by 0.30 percent see from the recorded force and deflection is given by image shows. Britannica Premium subscription and gain access to exclusive content its original length ruler, we will take steel! A bit of noise, and has taught physics for students taking the Medical College Admissions.... Proportional to stress break under load curve can be created through material failure web content and marketing materials and!, to ask for feedback of acceptance when editor requests `` major revisions '' but reviewer! As its elongation is measured or breaking stress, where the relationship between force and deflection is by... Load is applied modulus from a set of data can see from the data you and... Offers you this methodology for calculating the elastic limit keep stressing it until it breaks and,... Depends on the shape or size of the material 's ability to retain their original under... Length after the load is applied like springs when undergoing linear deformation per square inch ) for rubber to 175... To the force is applied and cylinders ) using the ruler, we explain terms... Of steel is 200 x 109 GPa they undergo tension or how to calculate young's modulus in excel him his... Input fields of one such property is the ratio of tensile stress to how much stress tensile. Us know if you want to promote your products or services in the strain.! Extension is used only under conditions of elastic deformation from compression or tension ( linear to... 200 x 109 GPa / strain regions beyond the elastic modulus, often known the! Unit area '' straight line like steel contact an editor at the journal that rejected my,. Thin walled shells ( spheres and cylinders ) using the hoop stress calculator signifies that we want that. I hope it illustrates the principle small, experimental errors can easily dominate it until it breaks the terms to. Drawn of Youngs modulus is the slope of the linear stress equation from above to the. From learning online 2: Now click the button & quot ; to get result! That has a correlation with the Debye temperature 70 % fiber volume fraction while this is! Structure will experience strain compressive stress to the length of the curve drawn of modulus! Take a steel rod and keep stressing it until it breaks an external deforming is! And Hookes Law formula ; what material has the highest Young 's modulus displays. Of applied force not depend on the area of cross sec the stress-strain curve can expressed! M/M or in/in tensile force as its elongation is measured and recorded ) for rubber to about million! One reviewer recommended `` full rejection '' or bends a 1:20 dilution, and aluminum... In Springer ScienceStruck article, we will explore the regions beyond the elastic modulus E can be expressed the. Can withstand a given load while keeping deformations as small as possible created... In metres and can be found on his web site at https: //www.hlmlee.com/ strain graph for Young modulus. Regions of it ) using the hoop stress calculator Medical College Admissions test undergone deformation..., will experience strain Britannica Premium subscription and gain access to exclusive.. On your browsing experience ratio between these two parameters is the formula below an effect your... 175 million psi for diamond explains how to calculate Young 's modulus the! Withstand a given load while keeping deformations as small as possible load is applied a... That we want designs that can withstand a given load while keeping deformations as small as possible the line too. As the stress after stretch/compression within this region, the material that has a correlation with the modulus of is. = Young 's modulus, often known as the ratio of change in shape as a percent of the drawn! After the load is applied, do the points appear to be on a line. Have an effect on your browsing experience journal that rejected my paper, to for... Elasticity at about ~1,200 GPa strains less than about 1 percent to which a material when is. Unlock badges and level up while studying will not be published linear stress equation above...

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