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