Properties of Materials - Assignment Example

? Contents Index Pages Material Properties 2 2. Experiment using round piece of mild steel 4 3. Axial Load on rectangular section 6 4. Composite Materials 7 Properties of Materials (#496720) Material Properties 1. Density- Density is defined as the ratio of mass to volume of material. Different materials depending on the type of application used have different densities. For lightweight structures aluminium is used which has a density of 2700kg/m^3. For heavier structures requiring a more robust construction, carbon steels of density 7850kg/m^3 is used. Storage tanks and other structures operating in a corrosive environment would prefer the use of stainless steel material of density 8200kg/m^3. ((Bansal R.K, 1998) Measurement of densities is critical since a defective product with a cracks or porosity would indicate a different density. Determination of density of a component indirectly leads to the calculation of the total weight of the structure and the corresponding stress due to this self weight. 2. Stress and Strain- Stress is defined as the intensity of force or force per unit area. In an engineering design the maximum allowable stress for a particular material is predefined and is a function of its yield strength. Therefore when a member has stresses beyond the allowable range, the area resisting this force is increased to bring it within the allowable range. Strain is defined as defined as the elongation of a structure per unit length. Calculating the strain helps the design engineer in comparing the values with the maximum allowable deflection.( Timoshenko Stephen and Gere James, 2004) 3. Tensile and Compressive strength- When a force is applied on bar or a structure in such a manner that it forces it to elongate, the resulting stresses are tensile stress. The maximum value of this particular stress for a particular material is called Tensile strength. When the direction of forces is reversed the stress induced is called compressive stress and the maximum value of this stress is called compressive strength. Determining both these values helps the design engineer in calculating the maximum allowable stress for the structure both in tension and compression respectively.( Timoshenko Stephen and Gere James, 2004) 4. Elastic and plastic deformation (a) The graph shows a region in which the stress and strain increase proportionally up to the proportional limit. The behaviour of the material is linear till this point. (b) The strain increases rapidly and the material shows elastic behaviour up to the elastic limit. (c) Beyond this point a significant increase in strain has only a minor change in tensile force. The material at this point is yielding and the point at which this starts is called the yield point. (d) Beyond the yield point to the lower yield point the material show plastic behaviour with large change in strain showing no change or a partial dip in stress values. The material is thus encountering plastic deformation.( Timoshenko Stephen and Gere James, 2004) 5. Modulus of Elasticity- As discussed in the previous graph stress is directly proportional to strain up to the proportional limit i.e Stress ? Strain or Stress= E x Strain. E here represents the Modulus of Elasticity and is dependent on the nature of the material. The elongation for a bar of length L, cross sectional area A under the impact of a force P having modulus of elasticity as E is given by ?L= P*L/(A*E). Modulus of elasticity is therefore critical in evaluating deflections. ( Timoshenko Stephen and Gere James, 2004) Experiment using Round piece of mild steel ( Timoshenko Stephen and Gere James, 2004) Reading Load Extension Strain Stress 1 50 0.09 0.00046 0.10186 2 100 0.19 0.00097 0.20372 3 150 0.29 0.00149 0.30558 4 160 0.34 0.00174 0.32595 5 165 0.46 0.00236 0.33614 6 170 0.78 0.004 0.34632 7 180 0.84 0.00431 0.36669 8 190 0.91 0.00467 0.38706 9 200 0.98 0.00503 0.40744 10 210 1.07 0.00549 0.42781 11 220 1.24 0.00636 0.44818 12 230 1.49 0.00764 0.46855 13 240 1.88 0.00964 0.48892 14 250 2.39 0.01226 0.5093 15 255 3.95 0.02026 0.51948 16 260 4.94 0.02533 0.52967 Given Data: material – mild steel Original length-195mm Diameter-25mm Area of cross section=л/4*D^2=490.8 mm^2 (a) Modulus of Elasticity E=F x L/ (A x ?L) Here for a change of load (150-50) =100kN extension is (0.29-0.09) =0.20mm F=100kN, L=195mm, A=490.8mm^2, ?L=0.20 Hence E= 100x195/(490.8 x 0.20)= 198.6 kN/mm^2 (b) Stress at limit of proportionality Load at limit of proportionality is 165kN Limit of proportionality= L/A=165 x 10^3/490.8= 336.2 N/mm^2 (c) The yield stress Load at yield point is 175kN. Hence yield stress= Force/ area=175000/490.8= 356.6 N/mm^2 (d) The proof stress This is the stress causing a strain of 0.1% Extension at 0.1% strain= 195 x 0.1/100=0.195mm. Load at curve intercept of 0.1% strain is 178kN. Proof stress= 178000/ 490.8= 362 N/mm^2 (e) % elongation Gauge length= 195mm Extension = 4.94mm Percentage elongation= 4.94 x 100/195=2.53% (f) Failure stress at failure diameter of 18.5mm Reduced area= л x 18.5^2/4=268.8mm^2 Since ultimate stress occurs at 255 kN (per the next question) and since rest of the graph cannot be plotted using the available data one can assume the graph rises and falls to a failure load of around 240kN Hence Failure stress if the rod fails at 240kN is 240000/268.8= 892 N/mm^2 (g) Permissible stress for a factor of safety of 3 and ultimate stress of 255kN Factor of safety = ultimate stress/ allowable permissible stress i.e Permissible stress= Ultimate stress/ Factor of safety= 255/3=85kN/mm^2 Axial Load on Rectangular section (Timoshenko Stephen and Gere James, 2004) Given Data Axial load – 145kN, diameter of hole – 20mm diameter, 2 Nos, Esteel=210kN/mm^2 (a) Breadth of the bar (b) Allowable stress of the bar= 155N/mm^2 Area of cross section= 9 x b mm^2 Stress = Load /area 155=145000/ 9b i.e b= 104mm (b) Stress in the bar at section Y-Y will be the same at all cross sectional areas= 155kN/mm^2 (c) Shear stress in each bolt Load acting along each bolt= 145/2= 72.5kN Area of cross section= л/4 x 20^2=314.2 mm^2 Shear stress at each bolt= 72.5 x 1000/314.2= 230.8N/mm^2 (d) Extension in bar if original length was 4m Initial area of cross section=9b=935.5 mm^2 ?L= P x L/ A x E= 145 x 4000/( 935.5 x 210)= 2.95mm (e) Strain in bar= ?L/L=2.95/4000= 0.00074 Composite materials Composite materials are defined as the combination of two or more materials that act as a reinforcement, binder and filler to improve the overall properties of the parent product. Cement by its inherent nature tends to be brittle. When additional materials in the form of aluminium, asbestos, natural fibre or steel fibre are added there is an overall improvement in the properties of strength, stiffness, fatigue life, thermal conductivity, density and wear resistance.( Roylance David, 2000 ) The brittle nature of concrete is also reduced and it tends to yield better under the impact of loads. Composites available are in the form of fibrous, laminated and particulate forms.( Loos Alfred C, n.d) It is generally heterogeneous and anisotropic i.e has different properties in all the three different planes. The commonly available cement composites are the following 1. Asbestos cement- Asbestos cement composites have been used in the construction industry for over eighty years. The use of this is now on the decline primarily due to the health hazard associated with it and its tendency in causing cancer. Apart from this cheap asbestos is highly resistant to attack from chemicals. These possess high tensile strengths in the range of 0.5 to 1.0 Gn/m^2 and elastic modulus in the range of 150GN/m^2. Asbestos cement concrete is also resistant to fire and have an advantage that the preparation of this cement is relatively easy since asbestos adheres to the cement quickly.( Akers S.A.S and Garrett.G.G, 1983) 2. Glass reinforced Cement- As with other composites glass fibre reinforced concrete (GFRC) offers all the benefits of composites including fire resistance, lightweight and easiness of construction. Its consists of Portland cement mixed with silica sand aggregate, glass fibres to give the flexural and tensile strength and other polymers to increase toughness. GFRC weighs only about 5 to 25 pounds per square foot and hence reduces weight of structures considerably. (Stromberg, 2010) Its tensile strength of 1700N/mm^2 is 3-4 times higher than that of steel. Its modulus of elasticity is also about 10 times that of polypropylene and hence tendency of the structure to crack is very low. Since the glass fibre reinforced concrete can expand and contract without any restriction any kind of stresses induced by heat and moisture is reduced. 3. Natural Fibre Reinforced Concrete- The commonly used natural fibres are sisal, coir, bamboo, Jute, akwara and elephant grass. Coir from coconut husks is very resistant to natural weather. It also increases the Modulus of Rupture of concrete (MOR). Bamboo increases the ultimate tensile strength and the MOR of concrete. Composite concrete made of akwara has impact strength increased to 16 times that of unreinforced cement. Elephant grass is resistant to alkali attack and also increases the flexural and impact strength of the cement concrete. Natural fibres when compared to other fibres is best suited in so far as shrinkage is concerned due to effect in retarding the evaporation of water 4. Polymer Reinforced concrete- The most commonly used polymers in cement composites are polyester, vinyl ester, epoxy, phenolic, polyamide, polypropylene and others. The advantage it possesses over steel reinforced concrete is that steel fibres are susceptible to corrosion and ingress of moisture into the steel fibre areas can severely damage the structure. However the polymer reinforced concrete faces no such issues relating to corrosion. 5. Steel Fibre Reinforced Concrete- Steel fibre reinforced concrete improves the ductility of the concrete and has the capability of carrying significantly large stresses. Usually as the size of the aggregate goes beyond 5mm the flowability of this mixture tends to reduce. Increase in aspect ratio or l/d (length/ diameter) of these fibres also tend to retard the workability of the concrete mix. (Chanh Nguyen , n.d) An ideal steel fibre reinforced concrete would have a good workability trait and will also have the fibres distributed uniformly through the cement mix. However, one of the main problems of steel fibres as with other fibres is that these tend to clump together in certain areas. ( Chanh Nguyen , n.d) Clumping may be caused due to the fibres being added at a rapid pace preventing uniform dispersion, volume of fibres added being too high, the mixer being incapable of producing a decent mix and insertion of the fibres into the mixer before the actual cement concrete is present might lead to fibres clumping together into balls.( Davis Ben, 2007) Change in Static Mechanical Properties (i) Compressive strength- There is no significant change in compressive strength of the concrete mix with increase up to ranges of 25%. However post cracking ductility undergoes a sharp increase with the concrete mix able to absorb large energy loads. (Chanh Nguyen , n.d) (ii) Tensile Strength- Fibres in the concrete mix that are in the same direction as that of the tensile stress undergoes 133% increase in tensile strength. Randomly distributed fibres get a 60% increase in tensile strength. (iii) Flexural Strength- Flexural strength also known as modulus of rupture is used to determine the ability of a brittle material like concrete to resist fracture. This property of concrete is what is affected the most since it undergoes an increase in the range of 100%. In a load-deflection curve under flexure, the area under the curve can be used to measure flexure toughness and is also the energy required for the concrete mix to rupture. It has been found out that rough fibres with large aspect ratios tend to produce higher toughness values. (Chanh Nguyen , n.d) (iv) Impact Strength- This can be defined as total number of consistent loads acting on the member which cracks the member. The steel fibre reinforced slabs have impact strength 18 times that of plain slabs. (v) Permeability- Fibres in unstressed concrete are expected to reduce permeability or the ability of water to seep into the structure when compared to normal concrete (vi) Shrinkage- This type of plastic shrinkage occurs due rapid loss of water from the surface. This can cause formation and propagation of minute cracks in normal concrete. However the addition of fibers reduces the tendency of this crack propagation by increasing the tensile strength of the cement concrete. Reference Lists 1. Akers S.A.S and Garrett.G.G, 1983, Fibre-matrix interface effects in asbestos-cement composites, Journal of Material Science 18, p.p 2200-2208 2. Bansal R.K, 1998, Fluid Mechanics and Hydraulic Machines, p.2 3. Chanh Nguyen Van, n.d, Steel Fiber Reinforced Concrete, p.p 108-115 4. Davis Ben, 2007, Natural Fiber Reinforced Concrete, p.p 1-21 5. Guidebook to GFRC, 2010, Available at :http://www.4stromberg.com [Accessed 2nd February 2011] 6. Loos Alfred C, n.d, Introduction to Composite Materials, Michigan State University, pp 1-14 7. Roylance David, 2000,Introduction to Composite Materials, Massachusetts Institute of Technology, p.p 1-5 8. Timoshenko Stephen and Gere James, 2004, Mechanics of Materials, p.p 1-13 Read More