Module 2 Selection of Materials and Shapes. IIT, Bombay

Transcription

1 Module Selection o Materials and Shapes

2 Lecture Selection o Materials - I

3 Instructional objectives By the end o this lecture, the student will learn (a) what is a material index and how does it help in selection o material or a given application, and (b) how to develop material indices considering the appropriate material properties or an intended service. Selection o Materials Appropriate selection o material is signiicant or the sae and reliable unctioning o a part or component. Engineering materials can be broadly classiied as metals such as iron, copper, aluminum, and their alloys etc., and non-metals such as ceramics (e.g. alumina and silica carbide), polymers (e.g. polyvinyle chloride or PVC), natural materials (e.g. wood, cotton, lax, etc.), composites (e.g. carbon ibre reinorced polymer or CFRP, glass ibre reinorced polymer or GFRP, etc.) and oams. Each o these materials is characterized by a unique set o physical, mechanical and chemical properties, which can be treated as attributes o a speciic material. The selection o material is primarily dictated by the speciic set o attributes that are required or an intended service. In particular, the selection o a speciic engineering material or a part or component is guided by the unction it should perorm and the constraints imposed by the properties the material. The problem o selection o an engineering material or a component usually begins with setting up the target Function, Objective, Constraints, and Free Variables. The Function reers to the task that the component is primarily expected to perorm in service or example, support load, sustain pressure, transmit heat, etc. The Objective reers to the target such as making the component unctionally superior but cheap and light. In other words, the Objective reers to what needs to be minimized or maximized. The Constraints in the process o material selection are primarily geometrical or unctional in nature. For example, the length or cross-sectional area o a component may be ixed. Similarly, the service conditions may demand a speciic component to operate at or beyond a critical temperature that will prohibit use o materials with low melting temperature. The Free Variables reer to the available candidate materials.

4 Material Index (M) The Material Index (M) reers to an attribute (or a combination o attributes) that characterizes the perormance o a material or a given application. The material index allows ranking o a set o engineering materials in order o perormance or a given application. Development o a Material Index (M) or an intended service includes the ollowing steps. Initial Screening o Engineering Materials. Identiication o Functions, Constrains, Objectives and Free Variables. Development o a Perormance Equation. Use constraints to eliminate the ree variable(s) rom the perormance equation and develop the material index. Rank a suitable set o materials based on the material index. Example 1: Selection o Material or a Light and Strong Tie-Rod [Fig...1] Figure..1 Schematic presentation o a Tie-Rod with an axial tensile load, F Function: Tie-rod to withstand an axial tensile load o F Objective: Minimise mass (m) where m = ALρ, where ρ is the material density. Constraints: Free variable: Perormance Equation: (i) Length L is speciied, (ii) Must not yield under axial tensile load, F (i) Cross-sectional area, A, (ii) Material F A σ y, where y σ is the yield strength o any material, The Perormance Equation can be rewritten by substituting the cross-sectional area, A, as FLρ ρ m m (F)(L) (1) σ y σ y So to minimize mass, we have to minimize the term, ( ρ σ y ). Or other way, we can maximize the term ( σ y ρ) or the sake o our convenience (as the available material property charts are σ y vs.

5 ρ ormat). So the material index, M 1 ( ρ), in this case becomes and a material with higher value o M 1 is expected to perorm better in comparison to a material with lower value o M 1. It should be noted that the Material Index in this case provides a ratio between the ultimate tensile strength and the density o the material. Thus, the Material Index (M 1 ) would provide a premise to examine i a material with higher weight (density) has to be selected to ensure that the same has suicient strength to avoid ailure. σ y Example : Selection o Material or a Light and Sti Beam [Fig...] Figure.. Schematic presentation o a beam with a bending load, F Function: Beam to withstand a bending load o F Objective: Minimise mass (m) where m = b Lρ, where ρ is the material density. Constraints: Free variable: (i) Length L is speciied, (ii) Must not bend under bending load, F (i) Edge length, b, (ii) Material Perormance Equation: The Perormance Equation can be developed considering the act that the beam must be sti enough to allow a maximum critical delection, δ, under the bending load, F. Thus, the Perormance Equation can be given as F EI (C 1) δ L where δ is the maximum permissible delection, E is the young s modulus, I is the second moment o area. The stiness, S, o the beam, can be written as, S = F δ and the second moment 4 o area, I, can be written as, I = b 1. The Perormance Equation can now be rewritten by substituting one o the ree variables (edge length, b) as ()

6 0.5 1S ρ m (L) 0. 5 () C1L E 0.5 The material index, M ( E ρ), in this case becomes and a material with higher value o M is expected to perorm better in comparison to a material with lower value o M. In other words, the Material Index (M ) will depict i a material with higher weight (density) has to be selected to ensure that the same has suicient stiness (i.e. E) to avoid bending during service. Example : Selection o Material or a Light and Strong Beam [Fig...] Figure.. Schematic presentation o a beam with a bending load, F Function: Beam to withstand a bending load o F Objective: Minimise mass (m) where m = b Lρ, where ρ is the material density. Constraints: Free variable: (i) Length L is speciied, (ii) Must not ail under bending load, F (i) Edge length, b, (ii) Material Perormance Equation: The Perormance Equation can be developed considering the act that the beam must be strong enough so that it does not ail due to an applied bending moment, M, due to the load, F. Thus, the Perormance Equation can be given as M L I σ y (C ) b / (4) L where σ y is the yield strength o the material and I is the second moment o area. The second 4 moment o area, I, can be written as, I = b 1. The Perormance Equation can now be rewritten by substituting one o the ree variables (edge length, b) as

7 6M 6F m (L) ρ or m (L) ρ / / CL y CL (5) σ σ y The material index, M ( σ y/ ρ), in this case becomes and a material with higher value o M is expected to perorm better in comparison to a material with lower value o M. In other words, the Material Index (M ) allows the examination i a material with higher weight (density) has to be selected to ensure that the same has suicient strength (i.e. σ ) to avoid ailure during service. Example 4: Selection o Material or a Light and Sti Panel [Fig...4] Figure..4 Schematic presentation o a panel with a bending load, F Function: Panel to withstand a bending load o F Objective: Minimise mass (m) where m = w t L ρ, where ρ is the material density. Constraints: Free variable: (i) Length L is speciied, (ii) Must not bend under bending load, F (i) Panel Thickness, t, (ii) Material Perormance Equation: The Perormance Equation can be developed considering the act that the stiness o the panel is suicient to allow a maximum critical delection, δ, under the bending load, F. Thus, the Perormance Equation can be given as F (C δ EI ) L where δ is the maximum permissible delection, E is the young s modulus, I is the second moment o area. The stiness, S, o the beam, can be written as, S = F δ and the second moment o area, I, can be written as, I = wt 1. The Perormance Equation can now be rewritten by substituting one o the ree variables (panel thickness, t) as (6)

8 1/ 1Sw ρ m (L) 1/ (7) CL E The material index, M 4 ( E 1/ ρ), in this case becomes and a material with higher value o M 4 is expected to perorm better in comparison to a material with lower value o M 4. The above our examples depict the simple procedure to develop Material Indices or the selection o suitable material or various structural requirements. These Material Indices can be used subsequently to shortlist a range o suitable materials rom appropriate Material Property Charts in a graphical manner. The Material Property Charts display the combination o material properties like Young s modulus and density, strength and density, Young s modulus and strength, thermal conductivity and electrical resistivity, strength and cost, and so on. Figure..5 shows a typical Material Property Chart that displays Young s modulus (in GPa) vis-à-vis density (in Mg/m ) or a range o engineering materials in a log-log scale. Figure..5 Material Property Chart o Young s Modulus vis-à-vis Density []

9 Exercise Choose the correct answer. 1. The Material Index that can be used to select a suitable material or a light, sti panel is (a) ( E 1/ ρ) (b) ( 1/ E) ρ (c) ( ρ) E (d) ( E ρ). The Material Index that can be used to select a suitable material or a light, sti tie-rod is (a) ( ρ) E (b) ( E) ρ (c) ( E ρ) (d) ( ρ). The Material Index that can be used to select a suitable material or a light, sti beam is (a) ( E 1/ ρ) (b) ( 1/ E) ρ (c) ( ρ) σ E (d) ( E ρ) 4. The Material Index that can be used to select a suitable material or a light, strong beam is (a) ( σ / ρ) (b) ( / σ ) ρ (c) ( ρ) σ (d) ( E ρ) 5. The Material Index that can be used to select a suitable material or a light, cheap and strong beam is (a) ( σ / ρ C m ) (b) ( / C σ ) ρ (c) ( σ m ρ) m / / C (d) ( C m ρ σ ) Answers: 1. (a). (a). (a) 4. (a) 5. (a) Reerences 1. G Dieter, Engineering Design - a materials and processing approach, McGraw Hill, NY, M F Ashby, Material Selection in Mechanical Design, Butterworth-Heinemann, 1999.