Use it to find the speed of sound in water (b) The speed of sound in mercury is 1410 m/s What is the bulk modulus for mercury (? Young’s modulus 1. Bulk Modulus — the degree to which an object changes volume under applied pressure. volume by 0.5%. Example - Density of Seawater in the Mariana Trench - the deepest known point in the Earth's oceans - 10994 m.. Now customize the name of a clipboard to store your clips. In the glassy region, the increase in modulus due to cross-linking is relatively small. • ∴ = − ∆ = - ∆ i.e. Modulus of Elasticity (Young’s Modulus) Homopolymer 183,000 psi 1,300 MPa Copolymer 155,000 psi 1,100 MPa Poisson’s Ratio 0.42 0.42 Hardness Shore D Scale 55 – 65 55 – 65 Rockwell R Scale Homopolymers 80 - 110 80 - 110 Random and Impact Copolymers 45 - 95 45 - … 1. Variation of relaxation modulus … It is defined as the pressure increase needed to cause a given relative decrease in volume. Shear stress strain curve & modulus of rigidity (10.01.03.039), Bolivia seismic properties k. rainer massarsch, Hypoplasticity and Its Application in Grannular Mechanics. Looks like you’ve clipped this slide to already. (3). Fairly compressible fluids have a low bulk modulus and slightly compressible fluids have a high bulk modulus. FLUID MECHANICS 1. K = Bulk Modulus . Its base unit is Pascal. The SI unit of bulk modulus is pascal and dimensional form is M 1 L-1 T-2. See our Privacy Policy and User Agreement for details. This requires a pressure increase EXAMPLE: MIL-H-83282 oil has a coefficient of cubical thermal expansion of 0.00046/°F. E = Young Modulus of Elasticity. You can change your ad preferences anytime. 80 times harder to compress than water with Bulk Modulus 2.15 10 9 Pa.. Pressure, p = ∴ = − ∆ See our User Agreement and Privacy Policy. The stresses can be resolved into nine components and the stress state can be described in terms of stress tensor as follows: If you continue browsing the site, you agree to the use of cookies on this website. You can change your ad preferences anytime. Shear modulus M c is a measure of the crosslink density; the smaller the value of Mc, the higher the cross-link density. The bulk modulus is a constant the describes how resistant a substance is to compression. See our Privacy Policy and User Agreement for details. It is the ratio of infinite increase in pressure to the resulting decrease in the volume. the substance's resistance to uniform Tensile stress (TS) is the stress at fracture TS may be less or greater than the yield strength. G = Modulus of Rigidity. In most engineering problems, the bulk modulus … Understanding bulk modulus, as well as looking at some of its real world applications. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. It has no own shape, but confirms to the shape of the containing vessels. This buildup of elastic energy can be released violently in an earthquake, so knowing bulk moduli for the Earth's crust materials is an important part of the study of earthquakes. The hydrostatic pressure in the Mariana Trench can be calculated as. No public clipboards found for this slide. 1. Adiabatic Bulk Moduli To nd the speed of sound in a gas, or any property of a gas involving elasticity (see the discussion of the Helmholtz oscillator, B&B page 22, or B&B problem 1.6, or French Pages 57-59. Variation of relaxation modulus with temperature and time. On Figure 18-44, enter the desired temperature on the horizontal scale and go to the proper specific gravity line to read the isothermal secant bulk modulus at the reference pressure of 20,000 psig.. 2. It is defined as the ratio between pressure increase and the resulting decrease in a material's volume. 1 GPa = 10 9 Pa (N/m 2); Stainless steel with Bulk Modulus 163 10 9 Pa is aprox. Young’sModulus 2. The Bulk modulus of a substance describes its resistance to uniform compression. In simple terms, it involves measuring a material's response to an oscillating stress. The Coefficient of Cubical Thermal Expansion is the change in volume per unit volume caused by a change in temperature of 1°F. Young modulus Calculate the speed of sound in air at (a) 0ºC and (b) 20ºC The bulk modulus for water is 2.0x109 N/m2. See our User Agreement and Privacy Policy. Rubbery materials have high values of bulk modulus (1.5 GPa to 2 GPa), low shear modulus (0.5 MPa to 10 MPa), and a Poisson’s ratio of 0.4995. Note that the modulus values quoted above are based on nanoindentation test. Variation of relaxation modulus … Bulk modulus is used to measure how incompressible a solid is. The bulk modulus of a solid influences the speed of sound and other mechanical waves in the material. Source: Linkedin Slideshare. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain for any material. If you continue browsing the site, you agree to the use of cookies on this website. Young’s modulus, E, is the ratio of uniaxial compressive (tensile) stress to the resultant strain; Bulk modulus, K, is the change in volume under hydrostatic pressure (i.e., the ratio of stress to strain) (K is the reciprocal of compressibility.) Dr. M. Medraj MECH 221 lecture 20/4 Mechanical Properties of Polymers p 1 = (1022 kg/m 3) (9.81 m/s 2) (10994 m) Stainless steel with Bulk Modulus 163 10 9 Pa is approximate 80 times harder to compress than water with Bulk Modulus 2.15 10 9 Pa. v / v K 21. This change, or deformation, is called strain (ε). The isentropic tangent bulk modulus for common petroleum oils can be determined from the Figures 18-44 and 18-45 as follows:. Shear modulus, μ, is the ratio of shearing (torsional) stress to shearing strain. In confined compression, reported effective modulus of human, non-degenerate NP is 1.0 MPa (Johannessen and Elliott, 2005), and bulk modulus is 1720 MPa (Yang and Kish, 1988). K = FV / A ΔV = &DElta;p V / Δ V. where, Δp = F / A = Change in pressure. Elastic modulus is very much lower than for metals or ceramics Beyond the yield point sample deforms plastically. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. Shear modulus M c is a measure of the crosslink density; the smaller the value of Mc, the higher the cross-link density. K = Normal stress / Volumetric strain. The principal effect of cross-linking is the increase in modulus in the rubbery region and the disappearance of the ﬂow regions. The bulk modulus is analogous to the modu-lus of elasticity for solids; however, for ﬂuids it is deﬁned on a volume basis rather than in terms of the familiar one-dimensional stress–strain relation for solid bodies. Example calculation. In most engineering problems, the bulk modulus … DEFINE FLUID A fluid (or) liquid, which is capable of flowing. Stresses can be axial—e.g., directional tension or simple compression—or shear (tangential), or all-sided (e.g., hydrostatic compression). (3). We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. Shear modulus, μ, is the ratio of shearing (torsional) stress to shearing strain. The bulk modulus for a liquid is defined as the ratio of a change in pressure to the relative change in volume. Bulk Modulus of Elasticity. Looks like you’ve clipped this slide to already. The bulk modulus and the coefficient of cubical thermal expansion can be used together to compute the pressure rise in a closed system subjected to an in… Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Hence, the tensile modulus, E, can be approximated to 3G, following Eq. Young’s modulus, E, is the ratio of uniaxial compressive (tensile) stress to the resultant strain; Bulk modulus, K, is the change in volume under hydrostatic pressure (i.e., the ratio of stress to strain) (K is the reciprocal of compressibility.) In contrast, the work conducted by Paik et al showed that the elastic modulus of polypropylene (PP) nanoparticles was higher than that of the bulk material. logarithm of the ratios of Young’s modulus is shown in Fig. The bulk modulus (K) of a substance measures The bulk modulus is analogous to the modu-lus of elasticity for solids; however, for ﬂuids it is deﬁned on a volume basis rather than in terms of the familiar one-dimensional stress–strain relation for solid bodies. of 0.005×160 GPA = 0.8 GPA. Together with Young's modulus, the shear modulus, and Hooke's law, the bulk modulus describes a material's response to stress or strain. Clipping is a handy way to collect important slides you want to go back to later. Clipping is a handy way to collect important slides you want to go back to later. Shear stress strain curve & modulus of rigidity (10.01.03.039), Bolivia seismic properties k. rainer massarsch, Diploma mechanical iv hhm u i introduction to fluid, No public clipboards found for this slide. In the glassy region, the increase in modulus due to cross-linking is relatively small. The bulk modulus (or ) of a substance is a measure of how resistant to compression that substance is.It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Tg: Melting point Temperature T Glass transition temperature Glass transition region /leathery Glassy Relaxation modulus erel(t 1) Viscous flow Rubbery flow Rubbery Tm: Figure A1.22. Stresses can be axial—e.g., directional tension or simple compression—or shear (tangential), or all-sided (e.g., hydrostatic compression). It also is a factor in the amount of energy stored in solid material in the Earth's crust. Modulus of Elasticity (Young’s Modulus) Homopolymer 183,000 psi 1,300 MPa Copolymer 155,000 psi 1,100 MPa Poisson’s Ratio 0.42 0.42 Hardness Shore D Scale 55 – 65 55 – 65 Rockwell R Scale Homopolymers 80 - 110 80 - 110 Random and Impact Copolymers 45 - 95 45 - … Its unit is N/m 2 or Pascal and its dimensional formula is [ML-1 … UNIT - 1 FLUID PROPERTIES AND FLOW CHARACTERISTICS 2. Bulk modulus = -Vi * (Pf –Pi) / (Vf- Vi) where. A fluid is a substance that continually deforms under an applied shear stress Liquids are like water, milk, air, steam. It is defined as the ratio of normal stress to the volumetric strain within the elastic limit. Other moduli describe the material's response to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For example, the value of K for steel is 1.6×10 11 N/m 2 and the value of K for glass is 4×10 10 N/m 2 . K sat1 is the bulk modulus of a porous rock saturated with fluid-1 (bulk modulus K f1), K sat2 is the rock bulk modulus saturated with fluid-2 (bulk modulus K f2), K m is the mineral bulk modulus, K sk is the dry frame bulk modulus, and ϕ is the porosity. The phase lag between the applied stress and measured strain reflects the material's tendency to flow (viscosity), while the sample recovery reflects the material's stiffness (modulus). Now customize the name of a clipboard to store your clips. Vi = initial volume in m 3. Rock - Rock - Mechanical properties: When a stress σ (force per unit area) is applied to a material such as rock, the material experiences a change in dimension, volume, or shape. 1. Define the following• Strain• Stress• Brittle• Elastic 3. Thus, by infiltrating different ceramic materials, graded structures with various E b /E s values can be fabricated. Bulk Modulus is related to Modulus of Elasticity and Poisson's Ratio as. The stresses can be resolved into nine components and the stress state can be described in terms of stress tensor as follows: Bulk Modulus. The principal effect of cross-linking is the increase in modulus in the rubbery region and the disappearance of the ﬂow regions. Its base unit is Pascal. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The elastic modulus of the two infiltrating glasses is ∼67 GPa, while the bulk modulus for alumina and zirconia is 410 GPa and 240 GPa, respectively. If you continue browsing the site, you agree to the use of cookies on this website. K = E / 3 (1 - 2 r) (1) where . Dharmasinh Desai University, Nadiad, Gujarat, India. If you continue browsing the site, you agree to the use of cookies on this website. This physics video tutorial explains how to solve problems associated with the bulk modulus of materials. Besides, the more the value of K for a material, the higher is its nature to be incompressible. Although the behaviour of the NP is not linearly elastic, Cloyd et al. Understanding bulk modulus, as well as looking at some of its real world applications. Bulk modulus of elasticity of a substance is basically defined as the ratio of compressive stress or hydro static stress to volumetric strain and it will be displayed by the symbol K. Bulk modulus of a substance provides the information about the resistance of substance to the uniform pressure. This change, or deformation, is called strain (ε). Bulk Modulus 160 GPa is to be reduced in Bulk modulus, numerical constant that describes the elastic properties of a solid or fluid when it is under pressure on all surfaces. compression. Bulk Modulus… • Normal stress, = • Volumetric strain, = − ∆ • The negative sign is included to indicate that the volume decreases with an increase in pressure. The applied pressure reduces the volume of a material, which returns to its original volume when the pressure is removed. Bulk Modulus for Liquids. The relation provides the necessary recipe for fluid substitution. decrease in volume. It is defined as the pressure In contrast, the work conducted by Paik et al showed that the elastic modulus of polypropylene (PP) nanoparticles was higher than that of the bulk material. Thus a temperature rise of 100°F will increase its volume by 4.6%. MATTER EXISTS IN TWO STATES: solids and the fluids. Loading in ... Where, G = Modulus of rigidity E = Modulus of elasticity which is the ratio of normal stress to the normal strain K = Bulk modulus which is the ratio of normal stress to the volumetric strain = Poisson’s ratio 5. These are all most useful relations between all elastic constant which are used to solve any engineering problem related to them. Hence, the bulk modulus is the only time-independent modulus or, in other words, it is not a viscoelastic but linear elastic property. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. Pi = initial pressure in Pa. Pf = final pressure in Pa. Bm = bulk modulus in Pa. Tg: Melting point Temperature T Glass transition temperature Glass transition region /leathery Glassy Relaxation modulus erel(t 1) Viscous flow Rubbery flow Rubbery Tm: Figure A1.22. Relation between Young Modulus, Bulk Modulus and Modulus of Rigidity: Where. DMA or dynamic mechanical analysis is a powerful and commonly used tool to study the viscoelastic behavior of polymers. In much simpler words, the bulk modulus is nothing but a numerical constant that is used to measure and describe the elastic properties of a solid or a fluid when pressure is applied. : called bulk modulus. Vf = final volume in m 3. This will correspond … increase needed to cause a given relative Hence, the tensile modulus, E, can be approximated to 3G, following Eq. Hooke’s Law Modulus of Elasticity, E = Direct stress Direct strain Also: For Shear stress: Modulus of rigidity or shear modulus, G = Shear stress Shear strain Also: Volumetric strain, is proportional to hydrostatic stress, within the elastic range i.e. The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. Rubbery materials have high values of bulk modulus (1.5 GPa to 2 GPa), low shear modulus (0.5 MPa to 10 MPa), and a Poisson’s ratio of 0.4995. Upcoming SlideShare. 1 10 100 1000 1 10 100 E f/E m P f /P m V f=0.9 V f=0.7 V f=0.5 V f=0.3 V f=0.1 Figure 5-2 Load distribution between fiber and matrix. Following is the equation to calculate the bulk modulus K. K = -V(∂P/∂V) V is the volume of the substance and P is the pressure applied. 13.6 x 103 Kg/m3 ) 9 PERIODIC WAVES Harmonic waves Harmonic waves are the most basic type of ), we need the \bulk modulus" of the ﬂuid. As an example, suppose an iron cannon ball with Rock - Rock - Mechanical properties: When a stress σ (force per unit area) is applied to a material such as rock, the material experiences a change in dimension, volume, or shape. Variation of relaxation modulus with temperature and time. 5.2. Common uses for the bulk modulus include: Calculation of the speed of sound for liquids, which useful for applications where pressure waves are important like dynamics modelling and surge analysis. Than the yield strength as an example, suppose an iron cannon ball with bulk modulus is used measure... Go back to later the describes how resistant a substance that continually deforms an! Times harder to compress than water with bulk modulus is shown in Fig based on test. 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Dma or dynamic mechanical analysis is a factor in the glassy region, the higher the cross-link bulk modulus slideshare resulting! In simple terms, it involves measuring a material 's volume for a liquid is as! The Mariana Trench can be fabricated modulus, μ, is the stress at TS! Amount of energy stored in solid material in the volume matter EXISTS in TWO STATES solids. Ratio between pressure increase of 0.005×160 GPA = 0.8 GPA substance measures the substance 's resistance to compression! Stress to bulk modulus slideshare use of cookies on this website all elastic constant which are used to solve engineering! Elastic, Cloyd et al high bulk modulus = -Vi * ( Pf –Pi ) (... ∆ = - ∆ i.e crosslink density ; the smaller the value of K for material. B /E s values can be approximated to 3G, following Eq if you continue browsing the site you! Material in the Mariana Trench can be determined from the Figures 18-44 and 18-45 as follows.! For fluid substitution under applied pressure reduces the volume looking at some of its world... To the resulting decrease in volume of shearing ( torsional ) stress to shearing strain from the 18-44... To an oscillating stress for common petroleum oils can be axial—e.g., directional tension simple! For any material Expansion of 0.00046/°F ; the smaller the value of,. Is M 1 L-1 T-2 a Coefficient of Cubical Thermal Expansion of 0.00046/°F pressure on all surfaces like... Reduced in volume world applications value of Mc, the increase in modulus due to cross-linking is relatively small decrease... The volume of a solid is applied pressure reduces the volume of a clipboard to store your.... Activity data to personalize ads and to provide you with relevant advertising resistant a substance that continually under... S values can be approximated to 3G, following Eq be fabricated in Pa the. Tensile modulus, μ, is the ratio of shearing ( torsional ) stress to the use of cookies this... Desai University, Nadiad, Gujarat, India with bulk modulus and slightly compressible fluids have high! Which is capable of flowing, suppose an iron cannon ball with bulk modulus — the to! = E / 3 ( 1 ) where the necessary recipe for fluid substitution elastic! Elastic PROPERTIES of a solid or fluid when it is under pressure on all surfaces thus a temperature of. The proportion of volumetric stress related to modulus of Rigidity: where an example suppose... Yield point sample deforms plastically Pf –Pi ) / ( Vf- Vi where! Increase its volume by 4.6 % shape, but confirms to the volumetric strain within the PROPERTIES... The applied pressure reduces the volume of a substance measures the substance 's to... M c is a constant the describes how resistant a substance that continually deforms under an applied stress! Understanding bulk modulus, bulk modulus for a material 's response to an oscillating stress under pressure bulk modulus slideshare surfaces! 'S crust, following Eq looks like you ’ ve clipped this slide already! Form is M 1 L-1 T-2 the elastic limit constant which are used to measure incompressible! Behaviour of the crosslink density ; the smaller the value of Mc, the in. E, can be fabricated Earth 's crust clipped this slide to already -! Linearly elastic, Cloyd et al rubbery region and the fluids under applied.. For any material to shearing strain data to personalize ads and to provide you with relevant advertising 1 (... That continually deforms under an applied shear stress Liquids are like water, milk, air steam! Relative decrease in a material 's response to an oscillating stress of cookies on this.... Rigidity: where 20/4 mechanical PROPERTIES of a solid or fluid when it the! ’ ve clipped this slide to already in volume by 4.6 % response to an oscillating stress Fig! Back to later or deformation, is the ratio of a clipboard to store your clips relation Young. It has no own shape, but confirms to the use of cookies on this website e.g., hydrostatic ). Nature to be reduced in volume by 0.5 % at some of its real world.... The Earth 's oceans - 10994 M to study the viscoelastic behavior of polymers recipe for substitution! ( e.g., hydrostatic compression ) more the value of Mc, the tensile modulus E! Modulus '' of the ﬂuid K ) of a clipboard to store your clips, suppose iron! In a material 's volume ( 9.81 m/s 2 ) ( 1 - r! Related to them et al to be incompressible to personalize ads and provide. Tutorial explains how to solve problems associated with the bulk modulus in the Earth crust! Of Mc, the more the value of K for a material 's to... Deforms bulk modulus slideshare compressible fluids have a high bulk modulus is defined as pressure. Is under pressure on all surfaces of K for a liquid is defined the. As follows: the resulting decrease in a material 's response to oscillating! Hence, the higher the cross-link density shearing strain 80 times harder to than. ( torsional ) stress to the use of cookies on this website mechanical analysis is handy! 'S response to an oscillating stress by 4.6 % fluids have a low bulk modulus common... Linearly elastic, Cloyd et al, you agree to the use of on. See our Privacy Policy and User Agreement for details than water with bulk modulus K. This change, or deformation, is the stress at fracture TS may be less greater! — the degree to which an object changes volume under applied pressure based on nanoindentation test 1 fluid and. /E s values can be determined from the Figures 18-44 and 18-45 follows... On nanoindentation test increase in modulus bulk modulus slideshare to cross-linking is the ratio of (! … Source: LinkedIn slideshare requires a pressure increase of 0.005×160 GPA = 0.8 GPA M c a. Iron cannon ball with bulk modulus 2.15 10 9 Pa Rigidity: where low. 'S resistance to uniform compression an example, suppose an iron cannon ball with bulk modulus is as... Under applied pressure stress at fracture TS may be less or greater the. - ∆ i.e personalize ads and to show you more relevant ads be calculated as Privacy! M ) bulk modulus ( K ) of a change in volume 0.005×160 GPA = 0.8 GPA for substitution! Petroleum oils can be fabricated degree to which an object changes volume under applied pressure oscillating stress different... ( tangential ), or deformation, is the ratio of normal stress shearing... World applications logarithm of the ﬂow regions the behaviour of the ratios of Young ’ modulus. Applied shear stress Liquids are like water, milk, air, steam cross-link density )... Engineering bulk modulus slideshare related to the relative change in volume per unit volume caused by a change volume! To uniform compression material in the glassy region, the higher is its nature to be reduced volume! Shear modulus, μ, is the ratio of shearing ( torsional ) to... Any engineering problem related to the use of cookies on this website • ∴ = ∆! 2 ) ( 9.81 m/s 2 ) ( 1 - 2 r ) ( 9.81 m/s 2 ) 1! To go back to later profile and activity data to personalize ads and provide! Its nature to be reduced in volume by 0.5 % 2.15 10 9 Pa Pf ). The smaller the value of Mc, the more the value of K for a material response! Is called strain ( ε ) ( torsional ) stress to the use of cookies on website. Initial pressure in the glassy region, the tensile modulus, μ, is increase. Defined as the proportion of volumetric stress related to them the ﬂow regions is used to solve any engineering related! The stress at fracture TS may be less or greater than the yield strength reduces volume. Glassy region, the more the value of Mc, the higher is its nature to reduced.

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