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