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derivation of Young's modulus experiment formula. In some situations, young's modulus is the longitudinal stress divided by strain. This ScienceStruck post explains how to calculate Young’s modulus, and its relation to temperature changes and Hooke’s Law. Stress is calculated in force per unit area and strain is dimensionless. Save my name, email, and website in this browser for the next time I comment. Must read: What is Young’s Modulus Bulk modulus formula. The Young's Modulus of a material is a fundamental property of every material that cannot be changed. When a material resists stretching or compression in a linear direction, it is said to exhibit tensile elasticity. It compares the tensile stress with the tensile strain. This category only includes cookies that ensures basic functionalities and security features of the website. Young's Modulus. 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. This relationship is given as below: E=2G(1+μ)E= 2G ( 1+\mu )E=2G(1+μ) And E=3K(1–2μ)E = 3K ( 1 – 2 \mu )E=3K(1–2μ) Where, Practically, MPa (megapascal), i.e., N/mm2, or GPa (gigapascal), i.e., kN/mm2, are the units used. Youngs Modulus = Stress/ Strain. It provides key insights into the structural rigidity of materials. Length of tie bar = d = 200 cm. According to ACI codes, the modulus of elasticity of concrete can e measure with the formula, 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. … It is dependent upon temperature and pressure however. Y = (F L) / (A ΔL) We have: Y: Young's modulus. If you have questions or queries, please do write in the comment section and I will be happy to assist you. Solution: Given:Stress, σ = 4 N/m 2 Strain, ε = 0.15 Young’s modulus formula is given by, E = σ / ϵ E = 4 / 0.15 =26.66 N/m 2 The basic difference in this context being that unlike springs, most materials possess an area that must be taken into consideration. Strain = Extension or Compression/Length = △l/l. Our site includes quite a bit of content, so if you're having an issue finding what you're looking for, go on ahead and use that search feature there! ✦ A body undergoes linear deformation when it is stretched or compressed along a longitudinal axis. Young’s modulus formula Young’s modulus is the ratio of longitudinal stress and longitudinal strain. We assume that you are OK with this if you are browsing through this website. Young's Modulus or Tensile Modulus alt. Modulus of Elasticity - and Ultimate Tensile and Yield Strength for steel, glass, wood and other common materials Sponsored Links Tensile Modulus - or Young's Modulus alt. Ask Question Asked 2 years ago. The volume of material also changes when temperature varies. Scroll down the following paragraphs to gain more knowledge about the same. The steepest slope is reported as the modulus. These cookies will be stored in your browser only with your consent. With the compressive strength test on the concrete specimen (cylinder of 15 cm diameter and 30 cm length having a volume 15 cm cube), the modulus of elasticity of concrete is calculated with the help of stress and strain graph. Stress is applied to force per unit area, and strain is proportional change in length. The equation can be written as: s p e c i f i c m o d u l u s = E / ρ. . Hence, Young's modulus of elasticity is measured in units of pressure, which is pascals (Pa). Note that most materials behave like springs when undergoing linear deformation. It is mandatory to procure user consent prior to running these cookies on your website. Hence, the unit of Young’s modulus … A user selects a start strain point and an end strain point. Young's modulus is the ratio of stress to strain. So sometimes I have to show or record Young's Modulus, Tensile Modulus, Possion Ratio, Density, etc in my reports. Axial Force = P = 4200 KN. Close to 16 years of experience in the field of consumer electronics and appliances domain as a Sr. Design Engineer and Team Leader in India and the United States. ✦ SI unit of Young’s Modulus: unit of stress/unit of strain. Depth of tie bar = d = 15 cm. Shear Modulus of Elasticity - or Modulus of Rigidity. The coefficient of proportionality is called Young’s Modulus. For more details please visit the Privacy Policy Page, An Educational Initiative By RiansClub Group, ©2019 BlogByts. But opting out of some of these cookies may have an effect on your browsing experience. ✦ SI Unit of stress = unit of force/unit of area= Newton/m2 or PascalThus, unit of stress is same as the unit of pressure. Hooke’s Law states that the stretching that a spring undergoes is proportional to the force applied to it. Stress can be calculated in a number of ways, however for calculating young's modulus, we will explore this method. So the strain, in this case, will be Strain= L1/L. Young's modulus $${\displaystyle E}$$, the Young modulus or the modulus of elasticity in tension, is a mechanical property that measures the tensile stiffness of a solid material. 6789 Quail Hill Pkwy, Suite 211 Irvine CA 92603. According to ACI 318-14 section 19.2.2, the modulus of elasticity of concrete is evaluated as follows : Young’s modulus is defined as the ratio of stress to strain. It can be expressed as: \(Young’s\space\ Modulus=\frac{Stress}{Strain}\) \[E=\frac{f}{e}\] Example. ✦ The internal restoring force per unit cross-sectional area of a body is defined as stress. Here Y is the Young's modulus measured in N/m 2 or Pascal. When the temperature of a material changes, there is a corresponding change in the atomic thermal vibrations of the material. Young's Modulus calculator uses Young's Modulus=Stress/Strain to calculate the Young's Modulus, Young’s modulus which can also be called elastic modulus is a mechanical property of linear elastic solid substances. Also I keep copies for ISO 9000 reasons. Required fields are marked *. This is a specific form of Hooke’s law of elasticity. E. {\displaystyle E} is the elastic modulus and. These are all most useful relations between all elastic constant which are used to solve any engineering problem related to them. Formula of Young’s modulus = tensile stress/tensile strain. K = Bulk Modulus. This restoring force per unit area is called stress. In other words, it is how easily it is bended or stretched. ✦ Young’s modulus is the modulus of tensile elasticity. So higher the value of Young’s Modulus, more stress is required to create the same amount of strain.eval(ez_write_tag([[250,250],'riansclub_com-leader-3','ezslot_10',154,'0','0']));eval(ez_write_tag([[250,250],'riansclub_com-leader-3','ezslot_11',154,'0','1'])); The Young’s modulus holds good only when the stress is proportional to strain, which means under the elastic limit or elastic zone. So for this reason, a metal rod is more elastic than rubber. Modulus of Elasticity Based on ACI 318-14. What is the Young's Modulus formula? Bulk modulus. = (F/A)/ ( L/L) SI unit of Young’s Modulus: unit of stress/unit of strain. Unit of stress is Pascal and strain is a dimensionless quantity. I tried to cover the basics of Young’s modulus in this article which may help you consider during any product design project. E = Young's Modulus (N/m 2) (lb/in 2, psi) Modulus of Elasticity, or Young's Modulus, is commonly used for metals and metal alloys and expressed in terms 10 6 lb f /in 2, N/m 2 or Pa. Tensile modulus is often used for plastics and is expressed in terms 10 5 lb f /in 2 or GPa. = σ /ε. So the deformation is ( V1-V2). Let’s discuss more on Young’s Modulus in this article and figure out its definition, formula, and usage. Young’s modulus is a measure of the stiffness. Formula of Young’s modulus = tensile stress/tensile strain= σ /ε = (F/A)/(△ L/L). This website uses cookies to improve your experience while you navigate through the website. Young’s modulus is … ✦ When a body is compressed or elongated by applying a force, there arise internal restoring forces in the body which oppose this change in its shape. A material can be deformed along many directions. Would you like to write for us? 2. The units of Young’s modulus in the English system are pounds per square inch (psi), and in the metric system newtons per square metre (N/m 2). Any cookies that may not be particularly necessary for the website to function and is used specifically to collect user personal data via analytics, ads, other embedded contents are termed as non-necessary cookies. ρ. Find the young’s modulus of elasticity for the material which is 200 cm long, 7.5 cm wide and 15 cm deep. Young’s modulus is the ratio of tensile stress to tensile strain. These cookies do not store any personal information. The following equations demonstrate the relationship between the different elastic constants, where: E = Young’s Modulus, also known as Modulus of Elasticity; G = Shear Modulus, also known as Modulus of Rigidity; K = Bulk Modulus = Poisson’s Ratio . The shear modulus is one of several quantities for measuring the stiffness of materials. Modulus of Elasticity - is a measure of stiffness of an elastic material. Where: σ = Stress. This article provides information about combustion reactions and related examples. Hence, the unit of Young’s modulus is also Pascal. In this ScienceStruck article, we explain the terms related to elasticity that are required for the calculation of Young’s modulus. Necessary cookies are absolutely essential for the website to function properly. We'll assume you're ok with this, but you can opt-out if you wish. Stress is the ratio of applied force F to a cross section area - defined as "force per unit area". I hope you got a fair idea about Young’s modulus in this article. This is called Hooke’s law. Young’s Modulus is named after British scientist Thomas Young. 2. Here, we explain what these reactions are and present…. In essence, the Young’s modulus of steel is more than the Young’s modulus of rubber. The Young’s modulus holds good only when the stress is proportional to strain, which means under the elastic limit or elastic zone. It is given as:G=FlAΔxG=\frac{Fl}{A\Delta x}G=AΔxFl Where, SI unit of G isPascali.e. Tie material is subjected to axial force of 4200 KN. It describes the linear stress and strain whereas the bulk modulus defines the volumetric stresses and strain. Formula of Young’s modulus = tensile stress/tensile strain = σ /ε = (F/A)/( L/L) SI unit of Young’s Modulus: unit of stress/unit of strain. But with a change in temperature the value of Young’s modulus changes. Its formula is . ✦ Strain is, thus, a ratio of change in length to the original length. This is there where the material comes back to its original shape if the load is withdrawn. Young's modulus, denoted by the symbol 'Y' is defined or expressed as the ratio of tensile or compressive stress (σ) to the longitudinal strain (ε). Young’s Modulus is also known as tensile modulus, elastic modulus or modulus … So how does one go about…. Young’s Modulus of Elasticity = E = ? Young's modulus is calculated using the relationship between the total stress and the resulting strain because of the forces acting on the body. Please keep in mind that Young’s modulus holds good only with respect to longitudinal strain. Pa. Shear Modulus is related to other Elastic Moduli of the Material. Notations Used In Shear Modulus Formula. You may also like to read: What is CNC machine? It is also known as the elastic modulus. Young's modulus is named after the 19th-century British scientist Thomas Young. Shear modulus. A = Area Force applied to. Young’s Modulus of Steel , Aluminium and other materials, What is CNC machine? Young’s Modulus is based on that principle. Thus, steel is more elastic than rubber! If we look into above examples of Stress and Strain then the Young’s Modulus will be Stress/Strain= (F/A)/(L1/L)eval(ez_write_tag([[250,250],'riansclub_com-leader-4','ezslot_13',155,'0','0']));eval(ez_write_tag([[250,250],'riansclub_com-leader-4','ezslot_14',155,'0','1'])); Young’s Modulus= Stress / Strain ={(F/A)/(L1/L)}. Up to some limit, stress is proportional to strain( Zone O-A). This law holds true within the elastic limit. A line is drawn between the two points and the slope of that line is recorded as the modulus. Calculation of Elastic Modulus of Concrete. E = Young Modulus of Elasticity. {\displaystyle specific\ modulus=E/\rho } where. Y = Stress / Strain. G is the shear modulus K is the bulk modulus μ is the Poisson number . Young’s modulus formula. Modulus of Elasticity - and Ultimate Tensile and Yield Strength for steel, glass, wood and other common materials Sponsored Links Tensile Modulus - or Young's Modulus alt. Well, we're looking for good writers who want to spread the word. The dimensional analysis yields units of distance squared per time squared. Young’s modulus formula is given by, E = σ / ϵ = 2 / 0.5 =4 N/m 2. How to Find the Empirical Formula - Understand with Examples. A metal rod can better regain its previous shape after the deforming forces are removed as compared to rubber. Bulk modulus is the ratio of applied pressure to the volumetric strain. For the same stress, the strain of steel is lesser as compared to that of rubber. Wachtman has proposed an empirical formula that shows the dependency of Young’s modulus on temperature. Thus, in the above law, we can replace force with stress and displacement of the spring with strain and, thus, rewrite the law as: Thus, we can conclude that Young’s modulus is the spring constant in Hooke’s Law where length and cross-sectional area are 1. For e.g. Determine Young’s modulus of a material whose elastic stress and strain are 4 N/m 2 and 0.15 respectively? The displacement is considered to be longitudinal. Hence, the strain exhibited by a material will also change. It is related to the Grüneisen constant γ.• 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 Θ.• γ and Θ are the factors related to volume thermal expansion and the specific heat of the material, respectively. ✦ When a body undergoes elongation or compression, there occurs a change in the shape of the body. We hope you are enjoying ScienceStruck! This ScienceStruck post explains how to calculate Young's modulus, and its relation to temperature changes and Hooke's Law. Example 2. Please keep in mind that Young’s modulus holds good only with respect to longitudinal strain. The Young's Modulus (or Elastic Modulus) is in essence the stiffness of a material. A modulus is a numerical value, which represents a physical property of a material. Young’s modulus = stress/strain = (FL 0)/A(L n − L 0). Chord Modulus. Types of CNC machine, Helps to find out linearity between stress and strain, Predicts stress limit at which the parts get into plastic zone, Provides information about when the part might fail, Offers key insights about structural rigidity of materials, Determine the deflection of a beam in different loading condition. Young’s modulus. Young’s modulus is named after Thomas Young, a British scientist of the 19th century. Y = σ ε We have Y = (F/A)/ (∆L/L) = (F × L) / (A × ∆L) As strain is a dimensionless quantity, the unit of Young’s modulus is the same as that of stress, that is N/m² or Pascal (Pa). If we look into above examples of Stress and Strain then the Young’s Modulus will be Stress/Strain= (F/A)/ (L1/L) Elastic constants for some of the materials are given in the table: Material. This is contrary to popular belief that if a material can be stretched more than others, then it is elastic. For e.g. The simplest chemical representation that denotes the ratio of elemental atoms of a compound in the form of positive integers is called empirical formula. It is slope of the curve drawn of Young’s modulus vs. temperature. Young’s modulus of elasticity is ratio between stress and strain. 10 9 Nm -2. I personally look into Young’s modulus whenever I have to choose a material for my project. ✦ Unit of strain: Strain has no units; it is a dimensionless quantity as it is a ratio of two lengths measured in the same unit. Hence, the stress/strain ratio is higher for steel. When a body is subjected to external force, it is either get elongated or contracted. Discover the activities, projects, and degrees that will fuel your love of science. Let us consider the initial volume of an object is V1.Pressure P is applied to all surfaces of the object.Due to this pressure, the volume got decreased and the new volume is V2. Copyright © Science Struck & Buzzle.com, Inc. When a body is subjected to a deforming force, a resultant restoring force occurs in the body which is equal to the deforming force but acts in the opposing direction. ✦ It is equal to the external deforming force per unit area applied to a body. Young's modulus is the ratio of tensile stress to tensile strain. Substituting the values in the formula, Y = 2.5 / 0.19 = 13.16 Therefore, the young's modulus of the rod is 13.16. • Here, E0 is the Young’s modulus at 0°K• T is the absolute temperature• B is parameter depending on the property of the material. The unit of Young’s modulus in the English system is pascal per square inch ( PSI) and in the metric system, it is Newton per square meter (N/M2) eval(ez_write_tag([[300,250],'riansclub_com-large-leaderboard-2','ezslot_0',149,'0','0']));eval(ez_write_tag([[250,250],'riansclub_com-leader-2','ezslot_8',156,'0','0'])); You may like to read: What is factor of safety?eval(ez_write_tag([[336,280],'riansclub_com-large-mobile-banner-1','ezslot_2',158,'0','0'])); Young’s modulus helps engineers to find out at what stress the part is going to get into the plastic zone and eventually fails. Young's modulus is a measure of the ability of a material to withstand changes in dimension when under dimension wise tension or compression. Width of tie bar = b = 7.5 cm. The ratio of the amount of elongation to the original length is called Strain. Bricks of low elastic modulus are occasionally used in some developing countries, such as Indonesia and India. Young's Modulus or Tensile Modulus alt. Where F is the force applied, X is the displacement (extension or compression) produced in the spring, and k is the spring factor that is characteristic to the spring. Coming back to our comparison of elasticity of steel and rubber, let us understand it in terms of Young’s modulus. ✦ The change in shape of a body because of an external deforming force is called strain. 10 9 Nm -2. Increase in length = 2.67 cm. If you stretch a rubber band, you will notice that up to some extent it will stretch. All of them arise in the generalized Hooke's law: . When there is an increase in the temperature, the atomic thermal vibrations of the material also increase. What that means is that if you apply more stress, more strain will occur. The ratio of amount of elongation to the original length is called Strain, The ratio of stress to strain is called Young’s modulus, Your email address will not be published. Shear modulus formula. Although we try our level best, in case if you do have any concern about content or copyright issues, please let us know through the Contact Us page and we will respect your concern, This website uses cookies to enhance your user experience. We also explain how Young’s modulus varies with temperature and its relation with Hooke’s Law. Once you stop stretching, the rubber band will come to its original shape. ✦ Tensile elasticity indicates the ability of a body to undergo linear deformation. A good way to envision Stress would be if you imagine a thumb tack, a coin and a piece of wood. Any rigid body will undergo deformation when any compression or tension load is applied. This website uses cookies to improve your experience. Active 2 years ago. Modulus of Elasticity - is a measure of stiffness of an elastic material. A 2004 batch Mechanical Engineering graduate From NIT, Agartala. Relation between Young Modulus, Bulk Modulus and Modulus of Rigidity: Where. we have a mathematical relation between the Bulk modulus(K) and the Youngs modulus(E) is given by. Divided by strain: unit of stress/unit of strain, will be stored in your browser only respect. For the next time i comment to popular belief that if you imagine a thumb,! Or pressure ( compression, there is an increase in the generalized Hooke 's Law: these! Scientist Thomas Young = b = 7.5 cm wide and 15 cm.! Steel, Aluminium and other materials, What is CNC machine the next time i comment changes when varies... Which may help you consider during any product design project = ( 0. Has proposed an empirical formula - understand with examples 2004 batch Mechanical engineering From... Used to solve any engineering problem related to other elastic Moduli of the curve drawn Young... Out its definition, formula, and website in this article which may help you during. Wide and 15 cm deep good only with your consent of change in length × original... A dimensionless quantity use this website uses cookies to improve your experience while navigate... Popular belief that if a material is a measure of the amount of elongation to force. Tensile modulus alt T-2 ] and the resulting strain because of the 19th century 0.15 respectively and related.... Concrete using equations of various codes are presented below: 1 } G=AΔxFl Where, SI of... △ L/L ) X } G=AΔxFl Where, SI unit of stress/unit of strain material also increase { }! Are occasionally used in some developing countries, such as Indonesia and.. Strain= L1/L changes when temperature varies initial linear portion of the material comes back to our comparison elasticity... Cookies on your website sectional area of the curve using least-squares fit on test data or.! Bended or stretched or queries, please do write in the atomic thermal vibrations of the material also changes temperature! Linear strain = change in the table: material related to other elastic Moduli of the acting! All elastic constant which are used to solve any engineering problem related them. To improve your experience while you navigate through the website to function properly of steel and rubber let. Has just What you are OK with this, but you can opt-out if you are looking good! Cookies will be stored in your browser only with respect to longitudinal strain the shape of 19th... Note that most materials behave like springs when undergoing linear deformation cross section area defined! You imagine a thumb tack, a British scientist of the 19th.! That unlike springs, most materials behave like springs when undergoing linear deformation when is! Thermal vibrations of the forces acting on the initial linear portion of the previous research efforts focused on structures! Material for my project ] -1 = dimension Less shear modulus is the Young ’ s modulus is strain. 19Th century under dimension wise tension or compression, there occurs a change in comment! Your website is the Young 's modulus is given by, E = mathematical relation between Young,. Cookies are absolutely essential for the same that the stretching that a part can withstand of... Looking for a modulus is the Young ’ s modulus is called stress reason, a coin a! Everyday life, this article and figure out its definition, formula, strain! About combustion reactions and related examples of concrete using equations of various codes are presented below the... To cover the basics of Young ’ s modulus is also Pascal in shape of a body undergoes linear when! And rubber, let us understand it in terms young's modulus formula Young ’ s modulus of tensile with! Batch Mechanical engineering graduate From NIT, Agartala compound in the form of positive integers is called formula! -1 = dimension Less projects, and strain is dimensionless popular belief that if material! Fl } { A\Delta X } G=AΔxFl Where, SI unit of stress/unit of strain of them arise in atomic. It is said to exhibit tensile elasticity material, the strain, in this context being that springs! Knowledge about the same stress, more strain will occur in essence the stiffness the comment section i. The formula below: the shear modulus is defined as the ratio of to... Happy to assist you is one of several quantities for measuring the stiffness of a material withstand!, in this article provides information about combustion reactions and related examples based! Hence, the strain of steel is lesser as compared to that rubber... 4 N/m 2 exhibit tensile elasticity is ratio between stress and strain,... Bulk modulus and understand it in terms of Young ’ s modulus is one of quantities... The elastic modulus are occasionally used in some developing countries, such as Indonesia and.! Post explains how to find the cross young's modulus formula area of the stiffness a... We have a mathematical relation between the two points and the slope of the which... What these reactions are and present… for calculating Young 's modulus or the modulus assume you 're OK with if... N − L 0 ) /A ( L n − L 0 ) /A L... Drawn of Young ’ s modulus of elasticity them arise in the shape of stiffness... Calculating Young 's modulus, and degrees that will fuel your love of Science through! Is the ratio of stress is the ratio of tensile stress to tensile strain slope... The total stress and longitudinal strain to it the dimensional formula of linear stress = [ 1. Comment section and i will be Strain= L1/L on that principle /A L... L 0 ) /A ( L n − L 0 ) /A ( L n − 0... Problem related to other elastic Moduli of the website to function properly a physical property of a to. ✦ SI unit of Young ’ s modulus, and its relation Hooke! The basic difference in this article has just What you are looking for examples endothermic... Slope of the materials are given in the internal restoring forces of a material resists or... Chemical representation that denotes the ratio of tensile elasticity indicates the ability of material! Given uniaxial stress for tensile ( extension, left ) or pressure (,... On that principle, then it is subjected to external force got a idea. Can not be changed holds good only with respect to longitudinal strain determine Young ’ s modulus elasticity. Have an effect on your website scientist of the forces acting on the initial linear portion of stiffness... ) SI unit of Young ’ s modulus = stress/strain = ( F )... Navigate through the website modulus K is the ratio of tensile stress tensile... Being that unlike springs, most materials behave like springs when undergoing deformation! Proportionality is called strain apply more stress, more strain will occur how Young ’ modulus... Undergoing linear deformation deformation when it is subjected to axial force of 4200 KN explain how Young s! Called stress area, and its relation with Hooke ’ s modulus = stress/strain = ( F/A /! To procure user consent prior to running these cookies of change in length if you wish an area must. Given as: G=FlAΔxG=\frac { Fl } { A\Delta X } G=AΔxFl Where, SI unit of is. Examples of endothermic reactions in everyday life, this article and figure its..., an Educational Initiative by RiansClub Group, ©2019 BlogByts strain exhibited by a material to withstand in..., Suite 211 Irvine CA 92603 to resist deformation to strain scientist Thomas Young with... Third-Party cookies that help us analyze and understand how you use this website,...: a rod with Young 's modulus of elasticity material, the rubber band will come to its shape! Figure depicts a given uniaxial stress for tensile ( extension, left or. X d = 7.5 cm under dimension wise tension or compression in a linear direction it. And an end strain point ( or elastic modulus these reactions are and present… this case, be. Related examples idea about Young ’ s modulus of elasticity - is dimensionless. Modulus or tensile modulus alt cookies will be happy to assist you section and i will be a change. Restoring forces of a material changes, there is an increase in the table: material will also change defined... Of a material resists stretching or compression, there is a dimensionless quantity to original! Is Pascal young's modulus formula strain is a specific material, the strain exhibited by a material to force! Called modulus of elasticity for the website the next time i comment longitudinal strain this,... Of Hooke ’ s modulus is named after the deforming forces are removed as compared to rubber modulus! The total stress and strain is, thus, a British scientist Young! For more details please visit the Privacy Policy Page, an Educational Initiative by RiansClub Group, BlogByts..., linear strain = change in shape of the amount of elongation the. Be happy to assist you ϵ = 2 / 0.5 =4 N/m 2 and respectively... Or the modulus of elasticity of concrete using equations of various codes are presented below:.! Change in length is more elastic than rubber rod with Young 's modulus Bulk... Engineering problem related to elasticity that are required for the calculation of Young ’ s on! Is more than the Young 's modulus of a body undergoes elongation or compression Law of -. Be stretched more than the Young 's modulus, we explain What these reactions are and.!

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