Chapter 7 Deforming Solids

Understand how tensile and compressive forces cause deformation Be able to describe the behaviour of springs and understand Hooke’s law Define and use stress, strain, and the Young modulus Describe an experiment to measure the Young modulus Be able to distinguish elastic and plastic deformation Demonstrate knowledge of force-extension graph for typical ductile, brittle and polymeric materials and be able to deduce the strain energy Objectives

Compressive and tensile forces A PAIR of forces are needed to change the shape of a spring When a spring is being squashed the forces are compressive, being pushed together When a spring is being stretched the forces are tensile, being pulled apart. When you bend a wire, some parts will be shorter and compressed, while others will stretched and under tension. When a spring is hanging with a load on it, the increase in the length of the spring is called the EXTENSION. Compressive and tensile forces

You plot the results of experiment by putting the extension on the horizontal axis and force on the vertical The gradient of the straight portion becomes the quantity known as the force constant of the spring Force constant = k = Newtons per meter K = F/x Spring constant = force/extention Hooke’s Law

Hooke’s law and elastic limit A stiffer spring (one that does not compress or undergo tension easily) will have a large value for the spring constant Beyond a certain point, if a force is applied the spring will be permanently deformed, it has stretched beyond its elastic limit. Hooke’s law – the extension produced in a material is proportional to the applied force (load). This is true of the material as long as the elastic limit is not exceeded. Hooke’s law and elastic limit

Investigating springs (your lab) Springs can be combined in different ways End to end (series) Side by side (parallel) In the experiment you will predict the outcome If the spring constant of a single spring is k, what will be the equivalent force constant of the two setups? Investigating springs (your lab)

Strain is defined as the fractional increase in the original length of a wire Strain = extension/ original legnth Strain = x/L The unit is a ratio (so %) Stress is the force applied per unit cross-sectional area of a wire Stress = force/ cross-sectional area Stress = F/A (measured in Pa) Stress and strain

The ratio of stress to strain is called the Young Modulus of the material E = σ/ε (sigma/epsilon) stress/strain E is measured in Pa Young Modulus

Determining Young Modulus Metals are not very elastic, most can only be stretched 0.1% of their original length To get the Young modulus of metal certain things should be done Use a long thin wire Extensions must be measured in meters from millimeters (very accurate To ensure accuracy, make sure you can do both Get a very accurate measurement of the cross sectional area (using a micrometer screw gauge capable of +_ 0.01mm) Determining Young Modulus

Determining Young Modulus Other materials like glass and plastic are stiff and brittle, making them difficult to measure Rubber can stretch, but their young modulus line is not straight, thus not very accurate Determining Young Modulus

Describing Deformation Glass and Cast iron Both are brittle, they stretch slightly before they break They have elastic behavior, before they break, they return to their original position Copper, Gold When these materials are stretched beyond their elastic limit, they do not return to their original length after the load is removed. Plastic Deformation These metals are described as ductile, able to be stretched bent, shaped. Iron is as well, but cast iron is not because of added carbon. Describing Deformation

Deformation continued Polythene, Perspex Different polymers behave differently depending on structure and temp. Polythene (plastic bags) have plastic deformation, but eventually becomes stiff and brittle. Behavior like ductile metal Perspex (acrylic glass) Brittle, stretches then breaks Rubber Rubber chords start off easy to stretch, but then becomes more difficult When the load is released on rubber, it does not return to its original length by the same path. Elastic hysteresis Work causes a rise in temperature, affecting the spring constant. Deformation continued

Elastic – return to their original length when the force is removed. Brittle materials break at their limit Ductile become permanently deformed if they are stretched beyond their elastic limit, they have plastic behavior summary

Strength of a material tells us about how much stress and strain is needed to break the materials. The value of breaking stress is called the Ultimate tensile stress. Brittle materials the UTS is the stress at the breaking point Strength of a material

Elastic Potential Energy The energy in a deformed solid, if the material has been strained elastically, the energy can be recovered Work has been done to move atoms against each other, creating some heat. Elastic potential energy can be determined using a force extension graph. Elastic Potential Energy

Finding Elastic potential energy Using the linear region of a graph where Hooke’s law is obey Used with the GRAPH Method 1 E = final force/2 x extention Method 2 = area = ½ base x height 1/2Fx The work done in stretching and compressing a material is always equal to the area under the graph of force against extention. Finding Elastic potential energy

Elastic potential energy found with spring constant Elastic potential energy = 1/2Fx = ½ x kx x x Elastic potenial energy = 1/2kx2 Elastic potential energy found with spring constant