## bulk modulus slideshare

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

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