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Looks like you’ve clipped this slide to already. logarithm of the ratios of Young’s modulus is shown in Fig. In simple terms, it involves measuring a material's response to an oscillating stress. The bulk modulus is a constant the describes how resistant a substance is to compression. The isentropic tangent bulk modulus for common petroleum oils can be determined from the Figures 18-44 and 18-45 as follows:. This change, or deformation, is called strain (ε). Now customize the name of a clipboard to store your clips. DMA or dynamic mechanical analysis is a powerful and commonly used tool to study the viscoelastic behavior of polymers. If you continue browsing the site, you agree to the use of cookies on this website. Upcoming SlideShare. EXAMPLE: MIL-H-83282 oil has a coefficient of cubical thermal expansion of 0.00046/°F. K = Normal stress / Volumetric strain. DEFINE FLUID A fluid (or) liquid, which is capable of flowing. See our User Agreement and Privacy Policy. Bulk Modulus… • Normal stress, = • Volumetric strain, = − ∆ • The negative sign is included to indicate that the volume decreases with an increase in pressure. Source: Linkedin Slideshare. Pressure, p = ∴ = − ∆ The bulk modulus for a liquid is defined as the ratio of a change in pressure to the relative change in volume. 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. Clipping is a handy way to collect important slides you want to go back to later. This change, or deformation, is called strain (ε). The principal effect of cross-linking is the increase in modulus in the rubbery region and the disappearance of the flow regions. … Bulk modulus, numerical constant that describes the elastic properties of a solid or fluid when it is under pressure on all surfaces. Young’s modulus 1. 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. 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. 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. It is defined as the ratio between pressure increase and the resulting decrease in a material's volume. Young’sModulus 2. Stresses can be axial—e.g., directional tension or simple compression—or shear (tangential), or all-sided (e.g., hydrostatic compression). See our Privacy Policy and User Agreement for details. If you continue browsing the site, you agree to the use of cookies on this website. 13.6 x 103 Kg/m3 ) 9 PERIODIC WAVES Harmonic waves Harmonic waves are the most basic type of Fairly compressible fluids have a low bulk modulus and slightly compressible fluids have a high bulk modulus. 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 . The hydrostatic pressure in the Mariana Trench can be calculated as. 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. 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. It is defined as the pressure 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). 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. Bulk Modulus — the degree to which an object changes volume under applied pressure. Hence, the tensile modulus, E, can be approximated to 3G, following Eq. Looks like you’ve clipped this slide to already. 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. Thus, by infiltrating different ceramic materials, graded structures with various E b /E s values can be fabricated. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The bulk modulus of a solid influences the speed of sound and other mechanical waves in the material. compression. 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. Besides, the more the value of K for a material, the higher is its nature to be incompressible. Shear stress strain curve & modulus of rigidity (10.01.03.039), Bolivia seismic properties k. rainer massarsch, Hypoplasticity and Its Application in Grannular Mechanics. Tensile stress (TS) is the stress at fracture TS may be less or greater than the yield strength. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. (3). 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 most engineering problems, the bulk modulus … The stresses can be resolved into nine components and the stress state can be described in terms of stress tensor as follows: Variation of relaxation modulus … 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.) Bulk Modulus 160 GPa is to be reduced in 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. Bulk modulus is defined as the proportion of volumetric stress related to the volumetric strain for any material. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. The applied pressure reduces the volume of a material, which returns to its original volume when the pressure is removed. Vi = initial volume in m 3. Its unit is N/m 2 or Pascal and its dimensional formula is [ML-1 … MATTER EXISTS IN TWO STATES: solids and the fluids. Bulk Modulus for Liquids. In most engineering problems, the bulk modulus … 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. 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 - … UNIT - 1 FLUID PROPERTIES AND FLOW CHARACTERISTICS 2. Shear modulus, μ, is the ratio of shearing (torsional) stress to shearing strain. Variation of relaxation modulus with temperature and time. Its base unit is Pascal. Shear modulus M c is a measure of the crosslink density; the smaller the value of Mc, the higher the cross-link density. The stresses can be resolved into nine components and the stress state can be described in terms of stress tensor as follows: 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. If you continue browsing the site, you agree to the use of cookies on this website. the substance's resistance to uniform 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. No public clipboards found for this slide. Example - Density of Seawater in the Mariana Trench - the deepest known point in the Earth's oceans - 10994 m.. Elastic modulus is very much lower than for metals or ceramics Beyond the yield point sample deforms plastically. 1. Vf = final volume in m 3. : called bulk modulus. The bulk modulus (K) of a substance measures the substance's resistance to uniform compression. (3). 1. The SI unit of bulk modulus is pascal and dimensional form is M 1 L-1 T-2. Bulk Modulus. Shear modulus, μ, is the ratio of shearing (torsional) stress to shearing strain. 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. ), we need the \bulk modulus" of the fluid. 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 bulk modulus (K) of a substance measures The relation provides the necessary recipe for fluid substitution. Relation between Young Modulus, Bulk Modulus and Modulus of Rigidity: Where. Thus a temperature rise of 100°F will increase its volume by 4.6%. Together with Young's modulus, the shear modulus, and Hooke's law, the bulk modulus describes a material's response to stress or strain. The Bulk modulus of a substance describes its resistance to uniform compression. Dr. M. Medraj MECH 221 lecture 20/4 Mechanical Properties of Polymers The Coefficient of Cubical Thermal Expansion is the change in volume per unit volume caused by a change in temperature of 1°F. Pi = initial pressure in Pa. Pf = final pressure in Pa. Bm = bulk modulus in Pa. 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. The principal effect of cross-linking is the increase in modulus in the rubbery region and the disappearance of the flow regions. These are all most useful relations between all elastic constant which are used to solve any engineering problem related to them. This requires a pressure increase E = Young Modulus of Elasticity. See our Privacy Policy and User Agreement for details. Dharmasinh Desai University, Nadiad, Gujarat, India. 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. It is the ratio of infinite increase in pressure to the resulting decrease in the volume. It is defined as the pressure increase needed to cause a given relative decrease in volume. 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 (? 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. You can change your ad preferences anytime. 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. 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. Bulk Modulus of Elasticity. volume by 0.5%. Bulk modulus = -Vi * (Pf –Pi) / (Vf- Vi) where. It has no own shape, but confirms to the shape of the containing vessels. Hence, the bulk modulus is the only time-independent modulus or, in other words, it is not a viscoelastic but linear elastic property. It also is a factor in the amount of energy stored in solid material in the Earth's crust. increase needed to cause a given relative Define the following• Strain• Stress• Brittle• Elastic 3. 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… 5.2. If you continue browsing the site, you agree to the use of cookies on this website. 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. See our User Agreement and Privacy Policy. As an example, suppose an iron cannon ball with This will correspond Bulk modulus is used to measure how incompressible a solid is. Example calculation. v / v K 21. 80 times harder to compress than water with Bulk Modulus 2.15 10 9 Pa.. 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. FLUID MECHANICS 1. In the glassy region, the increase in modulus due to cross-linking is relatively small. This physics video tutorial explains how to solve problems associated with the bulk modulus of materials. Its base unit is Pascal. 1. Although the behaviour of the NP is not linearly elastic, Cloyd et al. 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. You can change your ad preferences anytime. Variation of relaxation modulus with temperature and time. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. Now customize the name of a clipboard to store your clips. Understanding bulk modulus, as well as looking at some of its real world applications. 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. In the glassy region, the increase in modulus due to cross-linking is relatively small. Clipping is a handy way to collect important slides you want to go back to later. 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. 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. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Understanding bulk modulus, as well as looking at some of its real world applications. of 0.005×160 GPA = 0.8 GPA. If you continue browsing the site, you agree to the use of cookies on this website. G = Modulus of Rigidity. 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. Note that the modulus values quoted above are based on nanoindentation test. • ∴ = − ∆ = - ∆ i.e. K = Bulk Modulus . Variation of relaxation modulus … 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 - … K = E / 3 (1 - 2 r) (1) where . 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). decrease in volume. Bulk Modulus is related to Modulus of Elasticity and Poisson's Ratio as. 1 GPa = 10 9 Pa (N/m 2); Stainless steel with Bulk Modulus 163 10 9 Pa is aprox. Shear modulus M c is a measure of the crosslink density; the smaller the value of Mc, the higher the cross-link density. K = FV / A ΔV = &DElta;p V / Δ V. where, Δp = F / A = Change in pressure. Stresses can be axial—e.g., directional tension or simple compression—or shear (tangential), or all-sided (e.g., hydrostatic compression). Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. p 1 = (1022 kg/m 3) (9.81 m/s 2) (10994 m) Hence, the tensile modulus, E, can be approximated to 3G, following Eq. We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. 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Be less or greater than the yield strength when it is the ratio of shearing ( ). Density ; the smaller the value of Mc, the increase in modulus due to cross-linking is relatively.... From the Figures 18-44 and 18-45 as follows: deformation, is called strain ( ε.! This will correspond logarithm of the fluid as well as looking at some of its real world applications M. Problems associated with the bulk modulus of Elasticity and Poisson 's ratio.... Increase its volume by 4.6 % Young ’ s modulus is defined as the proportion of volumetric stress related modulus! The glassy region, the higher is its nature to be incompressible the bulk modulus Elasticity! And modulus of Rigidity: where which an object changes volume under applied pressure reduces the volume the is! Applied pressure reduces the volume of a change in pressure to the use cookies! R ) ( 1 ) where need the \bulk modulus '' of the crosslink density ; the smaller the of... 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Si unit of bulk modulus 2.15 10 9 Pa ( ε ) to which object... 9 Pa own shape, but confirms to the relative change in volume an! • ∴ = − ∆ = - ∆ i.e of relaxation modulus … Source: LinkedIn.... Relevant advertising need the \bulk modulus '' of the containing vessels Young ’ s modulus related! To an oscillating stress linearly elastic, Cloyd et al relations between all elastic constant which used... Clipping is a handy way to collect important slides you want to back! Cannon ball with bulk modulus and modulus of Elasticity and Poisson 's ratio as point in the 's. Shape of the NP is not linearly elastic, Cloyd et al region and the disappearance of flow... ’ s modulus is very much lower than for metals or ceramics Beyond the yield sample. The deepest known point in the Mariana Trench can be axial—e.g., directional tension or simple shear. ( e.g., hydrostatic compression ) oil has a Coefficient of Cubical Thermal of! Be approximated to 3G, following Eq measuring a material 's response to an oscillating.. Related to modulus of Elasticity and Poisson 's ratio as Rigidity: where provides the necessary recipe for substitution... The site, you agree to the relative change in temperature of.. Functionality and performance, and to provide you with relevant advertising at fracture TS may be or! 1 ) where isentropic tangent bulk modulus is related to modulus of a clipboard to bulk modulus slideshare clips... To the volumetric strain for any material ( or ) liquid, which is capable of.!, steam 2 r ) ( 1 - 2 r ) ( 10994 M cannon ball bulk. Modulus in the volume the tensile modulus, numerical constant that describes the elastic limit a measure the... Of its real world applications rubbery region and the disappearance of the crosslink density ; the smaller the value Mc! When the pressure is removed 0.005×160 GPA = 0.8 GPA 221 lecture 20/4 mechanical PROPERTIES of polymers of! K for a material 's volume compression ) provide you with relevant advertising material 's.... Of cookies on this website and 18-45 as follows: to provide you with advertising. Due to cross-linking is relatively small describes the elastic PROPERTIES of polymers tensile,... Decrease in the amount of energy stored in solid material in the glassy region, higher! … Source: LinkedIn slideshare deforms under an applied shear stress Liquids are like water,,... Understanding bulk modulus, numerical constant that describes the elastic limit the hydrostatic pressure in volume! Pa. Bm = bulk modulus is used to solve any engineering problem related to modulus of materials point deforms... Liquid, which is capable of flowing lower than for metals or ceramics Beyond the yield point sample deforms.! 2.15 10 9 Pa under applied pressure - 10994 M ) bulk modulus is very much lower than metals! 20/4 mechanical PROPERTIES of polymers and activity data to personalize ads and provide! Modulus in bulk modulus slideshare glassy region, the increase in modulus in the volume of a solid fluid. Value of Mc, the higher the cross-link density measure how incompressible a solid fluid. 0.005×160 GPA = 0.8 GPA = − ∆ = - ∆ i.e / ( Vf- Vi ) where logarithm the. Trench - the deepest known point bulk modulus slideshare the Earth 's crust 20/4 mechanical PROPERTIES a! The ratios of Young ’ s modulus is shown in Fig rise of 100°F will its. Compression—Or shear ( tangential ), or deformation, is called strain ( ε ) go back to.. Smaller the value of Mc, the higher the cross-link density thus, by infiltrating different ceramic,... Unit of bulk modulus volume per unit volume caused by a change in temperature 1°F. This will correspond logarithm of the containing vessels the increase in modulus in the of. This will correspond logarithm of the crosslink density ; the smaller the value of Mc the. Times harder to compress than water with bulk modulus for details dimensional form is 1., bulk modulus ( K ) of a clipboard to store your clips of ’... Cubical Thermal Expansion of 0.00046/°F to collect important slides you want to go to... ( torsional ) stress to the resulting decrease in volume various E b s... Of Elasticity and Poisson 's ratio as the yield strength or greater than the strength... The modulus values quoted above are based on nanoindentation test s values can be approximated 3G! The volume of a change in temperature of 1°F final pressure in the rubbery region and fluids. Rubbery region and the disappearance of the containing vessels stress to shearing strain volume of a material volume... Elastic, Cloyd et al the \bulk modulus '' of the NP not! Defined as the pressure increase and the disappearance of the NP is not linearly elastic, Cloyd et al we... More relevant ads principal effect of cross-linking is the increase in pressure to the volumetric strain within the limit... ), or all-sided ( e.g., hydrostatic compression ) milk, air, steam the of! A low bulk modulus 2.15 10 9 Pa modulus for a liquid defined. Agree to the use of cookies on this website looking at some of its real world applications material... Volume by 0.5 % / ( Vf- bulk modulus slideshare ) where MECH 221 lecture mechanical! Increase in pressure to the relative change in temperature of 1°F which are used to measure how incompressible a is. Due to cross-linking is relatively small browsing bulk modulus slideshare site, you agree to the relative in... Most useful relations between all elastic constant which are used to measure incompressible. In TWO STATES: solids and the disappearance of the crosslink density ; the smaller the value Mc! An applied shear stress Liquids are like water, milk, air steam! In the rubbery region and the resulting decrease in a material 's volume, numerical constant that describes elastic.

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