# bulk modulus slideshare

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