A tensile load is applied to a wire in small increments until it break. If each stress is plotted on a vertical coordinate and the corresponding strain (change in length) is plotted on the horizontal coordinate a curve is obtained. This is known as stress strain curve. It is useful to study some of the mechanical properties. Figure (1-8). strong stiff flexible ductile brittle weak R R: Resilience. T: Toughness. T Figure (1-9). The stress strain curve is a straight line up to point P after which it curves. The point P is the proportional limit, i.e. up to point P the stress is proportional to strain. Beyond P the strain is no longer elastic and so stress is no longer proportional to strain. Thus proportional stress can be defined as the greatest stress that may be produced in a material such that the stress is directly proportional to strain. The proportional limit deals with proportionality of strain to stress in the structure. Figure (1-10). Below the proportional limit (point P) the material is elastic in nature, that is, if the load is removed the material will return to its original shape. Thus elastic limit may define as the maximum stress that a material will withstand without permanent deformation. The elastic limit describes the elastic behavior of the material. It is defined as the stress at which a material exhibits a specified limiting deviation from proportionality of stress to strain. Yield strength often is a property that represents the stress value at which a small amount (0.l % or 0.2 %) of plastic strain has occurred. A value of either 0.1 % or 0.2 % of the plastic strain is often selected and is referred to as the percent offset. The yield strength is the stress required to produce the particular offset strain (0.1 % or 0.2 %) that has been chosen. As seen in Figure (1-11); the yield strength for 0.2 % offset is greater than that associated with an offset of 0.1 %. If yield strength values for two materials tested under the same conditions are to be compared, identical offset values should be used. To determine the yield strength for a material at 0.2 % offset, a line is drawn parallel to the straight-line region (see Figure 1-11), starting at a value of 0.002, or 0.2 % of the plastic strain, along the strain axis, and is extended until it intersects the stress-strain curve. The stress corresponding to this point is the yield strength. Although the term strength implies that the material has fractured, it actually is intact, but it has sustained a specific amount of plastic strain (deformation). Ultimate tensile strength: It is the maximum stress that a material can withstand before failure in tension. Ultimate compressive strength: It is the maximum stress that a material can withstand before failure in compression. UTS Figure (1-9): Stress strain plot for stainless steel orthodontic wire that has been subjected to tension. The proportional limit (PL) is 1020 MPa. Figure (1-11): Although not shown, the elastic limit is approximately equal to this value. The yield strength (YS) at a 0.2 % strain offset from the origin (O) is 1536 MPa and the ultimate tensile strength (UTS) is 1625 MPa. An elastic modulus value (E) of 192.000 MPa (192 GPa) was calculated from the slope of the elastic region. Once the elastic limit of a material is crossed by a specific amount of stress, the further increase in strain is called permanent deformation, i.e. the resulting change in dimension is permanent. If the material is deformed by a stress at a point above the proportional limit before fracture, the removal of the applied force will reduce the stress to zero, but the strain does not decrease to zero because plastic deformation has occurred. Thus, the object does not return to its original dimension when the force is removed. It remains bent, stretched, compressed, or otherwise plastically deformed. As shown in figure (1-11); the stress-strain graph is no longer a straight line above the proportional limit (PL), but rather it curves until the structure fractures. The stress strain graph shown in figure (1-11) is more typical of actual stress-strain curves for ductile materials. Unlike the linear portion of the graph at stresses below the proportional limit, the shape of the curve above (P) is not possible to extrapolate because stress is no longer proportional to strain. An elastic impression material deforms as it is removed from the mouth. However, due to its elastic nature it recovers its shape and little permanent deformation occurs. It represents the relative stiffness or rigidity of the material within the elastic range. It is the ratio of stress to strain (up to the proportional limit), so the stress to strain ratio would be constant. It therefore follows that the less the strain for a given stress, the greater will be the stiffness, e.g. if a wire is difficult to bend, considerable stress must be placed before a notable strain or deformation results. Such a material would possess a comparatively high modulus of elasticity. The metal frame of metal-ceramic bridge should have high stiffness. If the metal flexes, the porcelain veneer on it might crack or separate. Generally in dental practice, the material used as a restoration should withstand high stresses and show minimum deformation. However, there are instances where a large strain is needed with a moderate or slight stress. For example in orthodontic appliance, a spring is often bent a considerable distance under the influence of a small stress. In such a case, the structure is said to be flexible and it possesses the property of flexibility. The maximum flexibility is defined as the strain that occurs when the material is stressed to its proportional limit. It is useful to know the flexibility of elastic impression materials to determine how easily they may be withdrawn over undercuts in the mouth. It is the amount of energy absorbed by a structure when it is stressed not to exceed its proportional limit. Resilience can be measured by calculating the area under the elastic portion (straight line portion) of the stress strain curve calculating (the area of the triangle=1/2 bh). Resilience has particular importance in the evaluation of orthodontic wires. An example: The amount of work expected from a spring to move a tooth. It is the energy required to fracture a material. It is also measured as the total area under the stress strain curve (elastic and plastic portions of stress strain curve). Toughness is not as easy to calculate as resilience. Figure (1-12): The area under stress strain graph may be used to calculate either (a) resilience or (b) toughness. It is the relative inability of a material to sustain plastic deformation before fracture of a material occurs. Brittleness is generally considered as the opposite of toughness, glass is brittle at room temperature. It will not bend appreciably without breaking. It should not be wrongly understood that a brittle material is lacking in strength, from the above example of glass we see that its shear strength is low, but its tensile strength is very high, if glass is drawn into a fiber, its tensile strength may be as high as 2800 MPa. Ductile Brittle Nylon Acrylic Many dental materials are brittle, e.g. porcelain, acrylic, cements, gypsum products. It is the ability of a material to withstand a permanent deformation under a tensile load without rupture. A metal that can be drawn readily into a wire is said to be ductile. It is dependent on tensile strength. Ductility decrease as the temperature increased. Figure (1-13): Schematic of different type of deformation in brittle (glass, steel file) and ductile (copper) materials of the same diameter and having a notch of the same dimension. Figure (1-14): Stress strain plots of materials that exhibit different mechanical properties. (UTS) ultimate tensile stress, (PL) proportional limit. It is the ability of a material to withstand considerable permanent deformation without rupture under compression as in hammering or rolling into a sheet. It is not dependent on strength as is ductility. It increases with raise in temperature. Gold is the most ductile and malleable metal. This enables manufacturer to beat it into thin foils. Silver is the second. It is the reaction of a stationary object to a collision with a moving object. Impact strength: it is the energy required to fracture a material under an impact force. Dentures should have high impact strength to prevent it from breaking if accidentally dropped by patient. Pendulum A structure subjected to repeated or cyclic stress below its proportional limit can produce abrupt failure of the structure. This type of failure is called fatigue. Restorations (filling, crown, denture) in the mouth are subjected to cyclic forces of mastication, so these restorations should be able to resist fatigue. The hardness is the resistance to permanent surface indentation or penetration. The value of hardness, often referred to as the hardness number, depends on the method used for its evaluation. Generally, low values of hardness number indicate a soft material and vice versa. Used for measuring hardness of metal and plastic materials. Figure (1-15): Shapes of hardness indenter points (upper row and the indentation depressions left in material surfaces (lower row). The measured dimension M that is shown for each test is used to calculate hardness. The following tests are shown: Brinell test: A steel ball is used, and the diameter of the indentation is measured after removal of the indenter. Rockwell test: A conical indenter is impressed into the surface. Under a minor load (dashed line) anti a major load (solid line), and M is the difference between the two penetration depths. Vickers test: A pyramidal point is used, and the diagonal length of the indentation is measured. Knoop test: A rhombohedral pyramid diamond tip is used, and the long axis of the indentation is measured. Figure (1-17): Vickers indentation. Figure (1-18): Vicat penetrometer used to determine initial setting time of gypsum products. After a substance has been permanently deformed (plastic deformation), there are trapped internal stresses; such situations are unstable. The displaced atoms are not in equilibrium positions through a solid-state diffusion process driven by thermal energy, the atoms can move back slowly to their equilibrium positions, the result is a change in the shape or contour of the solid as the atoms or molecules change positions. The material warps or distorts. This stress relaxation leads to distortion of elastomeric impressions. Waxes and other thermoplastic materials like compound undergo relaxation after they are manipulated.