Copyright Joseph Greene Strength of Elastomers Professor Joe Greene CSU, CHICO

Copyright Joseph Greene Strength of Elastomers Introduction Initiation of Fracture Threshhold of Strengths and Extensibilities Fracture under Multiaxial Streses Crack Propagation Tensile Rupture Repeated Stressing: Mechanical Fatigue Surface Cracking by Ozone Abrasive Wear

Copyright Joseph Greene Initiation of Fracture Fracture is a highly selective process –Only a small number of those molecules making up the test piece actually undergo rupture. Questions –Where and under what conditions does fracture begin? –What laws govern the growth of a crack once it has been initiated? Initiation of fracture from flaws or points of weakness –Applied stress is greatly magnified –Fracture begins at such points –Propagation of the crack is dependent on the load applied and the geometry near the crack Rubber is viscoelastic –Mechanical properties depend upon the rate of deformation

Copyright Joseph Greene Initiation of Fracture Flaws and Stress risers –Every solid body has flaws or points of weakness Inhomogenity of composition or structure Sharp corners, nicks, cuts, scratches…. –Stress is locally higher in these regions If higher than strength of the material, it will break. –Stress concentration factor Ratio of the stress at the tip of a sharp flaw to the applied stress –Equation 1 Edge flaws are more serious stress raisers than enclosed flaws of the same size. Figure 1. Tip versus enclosed crack. Figure 2. Distance away from crack. Figure 3. Fatigue lives

Copyright Joseph Greene Initiation of Fracture Tensile Test Piece –Thin strip of thickness, t, with a cut in one edge of depth, l, is place in tension until it breaks. Figure 4 Effect of cut in diminishing the total stored elastic energy, U, can be calculated by –Reduction in stored energy = kl 2 tU, where k = pi/(1+strain) 1/2 Tear Test Piece –Test piece, Fig 5, has regions I in the arms that are in simple extension and II that is undeformed. –Work of fracture is GcA

Copyright Joseph Greene Threshhold Strengths and Extensibilities Lake and Lindley researchers found that –Minimum amount of mechanical energy is needed (about 50 J/m 2 ) for a crack to propagate at all. –Other researchers found range between J/m 2 –Threshold fracture energy, G 0 is a function of Molecular weight between crosslinks, M c. G 0 =  M c 1/2 Where  is a function of density of the polymer, the mass, length, and effective flexibility of the monomer unit.  is found to be about 0.3 J/m 2 (g/g-mole) -1/2 –For example, Mn=300,000, Mc =15,000, and , then G 0 =25 J/m 2 Increased crosslinking leads to higher E and then higher tensile strength which resists the fracture.

Copyright Joseph Greene Fracture Under Multiaxial Stresses Few studies concern the fracture of elastomers under complex stress conditions, though Compression and shear –Elastomers do not fail along shear planes. Fractures develop at 45 to the direction of the shear (Fig 6) –At right angles to the corresponding principle tensile stress and at a shear stress equal to the tensile strength. –General condition for rupture appears to be the attainment of a specific tensile stress at the tip of an existing flaw. No case of fracture has occurred under uniform triaxial compression loading when all compressive stresses are equal –Under uniaxial compression, a breaking stress 8X as in tension by growth of a crack in an oblique direction. Difficult to achieve uniaxial compression Instead, friction at the loaded surfaces of a thin compressed block prevents elastomer from expanding laterally, a bulge develops and tears. –Rubber block under compression is resistant to fracture, but stiffness is reduced by loss of rubber in outer regions

Copyright Joseph Greene Crack Propagation Crack propagation is widely different. –3 basic patterns of crack propagation correspond to elastomer type. Amorphous elastomers- SBR –Exhibit simple tearing behavior: Once fracture starts, a tear propagates at rate dependent upon strain energy release rate G and temperature, T. Crystallize on stretching- NR and Neoprene –Tear strength is enhanced over a range of tear rates and temperatures Reinforced elastomers with 30% fillers- carbon black –Particles cause an increase in tear strength and tensile strength by 10 fold over a range of rates and temperatures of test. –Dynamic (repeated) crack propagation Amorphous elastomers tear steadily at rates controlled by available energy, G, for fracture Strain crystallizing elastomers do not tear continuously under small values of G. Fig 19

Copyright Joseph Greene Tensile Rupture Effects of Rate and Temperature –Several relations are shown for breaking stress of unfilled SBR as a function of rate of elongation. Fig 20 Relationship forms parallel curves and into one Master Curve –Fig 21- Strength at a given temperature is equal to the strength at another temperature with a scale factor imposed. (In a log-log scale) –Fig 22- Master curve (WLF relationship for polymers Equation 19) is based upon reference temperature. Failure envelope for tensile rupture over range of T and rate of elongation –Plot breaking stress against corresponding breaking extension. –Yield a single curve, failure envelope, with a parabolic shape. »Follow curve in an anticlockwise sense corresponds to the rate of extension or to decreasing temperature »At Lower extreme, breaking stress and elongation are small as a result of a low rates of strain or at high temperatures. »At Higher extreme, breaking stress and elongation are large as a result of a high rates of strain or at low temperatures.

Copyright Joseph Greene Tensile Rupture Effects of Degree of Crosslinking –Breaking stress passes through a sharp maximum as degree of crosslinking is increased from zero. Fig 24 Due to changes in viscoelastic properties –Failure envelops for degree of crosslinking Scale breaking elongation e b in terms of its maximum value (dependent upon degree of crosslinking) Breaking stress is converted to a true stress at break rather than the engineering stress. (Note: true stress is divided by actual cross-sectional area during the test)

Copyright Joseph Greene Tensile Rupture Strain-crystallizing elastomers –Amorphous elastomers show steady fall in tensile strength as temperature is raised. –Strain-crystallizing elastomers show a rather sudden drop at a critical temperature, Tc. Fig 26. Tc depends strongly on the extent of crystallization Sharp drop at critical temperature is due to failure of material to crystallize at higher temperatures. It stays amorphous except at the tip. Similar to similar drop at critical depth. Fig 27. –Other aspects of Tc. The effect of a Tc is the same for compounds with fillers. Tc depends strongly on the type of crosslinking, being the highest for long, polysulfidic crosslinks and the lowest for carbon-carbon crosslinks.

Copyright Joseph Greene Tensile Rupture Energy Dissipation and Strength –General correlation between tensile strength and temperature interval (T-Tg) as in the WLF equation, has been well understood. T= test temp and Tg=glass transition temp –Example for polyurethane, Fig 28 As temperature increases away from Tg the tensile strength decreases linearly in log-log scale. –Energy dissipation and strength, Fig 29 Those materials that require the most energy to bring rupture (strongest elastomers) are those in which the major part of energy is dissipated before rupture causing heating or elastomer

Copyright Joseph Greene Repeated Stressing: Mechanical Fatigue Fatigue failure –Under repeated tensile deformations cracks appear in the edges of the specimen and grow across it in an accelerating way. Every time a deformation is imposed, energy G is available to cause a strain energy to cause growth by tearing of a small nick in the edge of the specimen. Corresponding growth step  l obeys equation 22 (proportional to G 2 ), then the crack growth becomes »  l/l = (4k 2 BU 2 )  n » Where n is the number of times the deformation is imposed, k is a numerical constant (about 2). –The depth of crack after N strain cycles is obtained by integration, and »l 0 -1 – l –1 = 4k 2 BU 2 N »Fig 30 for Growth of and edge and Fig 31 for Fatigue life

Copyright Joseph Greene Repeated Stressing: Mechanical Fatigue Fatigue failure –Examples of the dependence of fatigue life on an initial cut size are shown in Figs. 3 and 31. Lives for test pieces which contain no deliberately introduced cuts are represented by horizontal lines in Fig 3 –Interpreted as stepwise tearing from a hypothetical nick or flaw, 20 microns deep. Closely similar sizes of 20 microns are deduced natural flaws for both strain-crystallizing and non crystallizing elastomers For non-crystallizing elastomers (SBR), the crack growth is quite different over the main tearing region (Eqn 23) –Different crack growth rate for strain crystallizing (NR) and noncrystallizing (SBR) elastomers. Fig 32 »For SBR the fatigue life is more dependent on the size of the initial flaw and the magnitude of the imposed deformation. So that elastomers are generally longer-lived at small deformations and with no accidental cuts. Shorter lived under severe conditions.

Copyright Joseph Greene Repeated Stressing: Mechanical Fatigue Fatigue failure –Fatigue life is drastically lowered at high temperatures as a result of the sharp increase in the cut growth coefficient D as the internal viscosity is decreased. The hysteresis associated with strain-induced crystallization is retained, provided that the temp doesn’t get too high (100°C for NR) that crystallization no longer occurs. Fatigue life for NR is not greatly affected by rise in temp –Fatigue life is different between noncrystallizing and strain crystallizing elastomers when stress is not relaxed to zero during each cycle. Fig 33. Fatigue life for NR is greatly increased when minimum strain is raised when minimum strain is increased from 0 to 100% because the crystalline barrier to tearing at the tips of chance flaws does not then disappear in the min strain state. –The growth of flaws is virtually stopped unless the total applied strain is very large ( %) For noncrystallizing elastomers, no comparable strengthening occurs from raising the minimum strain.

Copyright Joseph Greene Surface Cracking by Ozone In ozone environment, –stretched samples of unsaturated elastomers develop surface cracks which grow in length and depth until failure. Even small cracks can cause reduction in strength and fatigue life. –Tensile stress necessary for an ozone crack is calculated »from Eqn 6 __  b =(G c E/  l) 1/2 for stress at break and »Eqn 7 for extension e b =(G c/ /  lE) 1/2 –Small amounts of fracture energy, G, of (0.1 J/m 2 ) is needed for cracks –Molecular scission occurs by reacting with the ozone. »Example, Soft rubber, E=2 MPa, effective length, l, = 40 microns, then Eqn 6 yields critical tensile stress of about 50 kPa and a critical strain of about 5%. Cracks occur when stress is higher. »As stress rises, more cracks form »Note: many smaller cracks are less harmful than fewer large cracks

Copyright Joseph Greene Abrasive Wear Mechanics of wear –Abrasive wear consists of the rupture of small particles of elastomer under action of frictional forces, when sliding takes place between elastomer surface and a substrate. Suitable measure of the rate of wear is ration of A/  –A is the volume of rubber abraded away per unit normal load and per sliding distance, and  is the coefficient of friction. –Abradability= abraded volume per unit of energy dissipated in sliding. Master curves for the dependence of abradability on the speed of sliding are created by means of WLF relation (Eqns. 18,19) Abradability decreases with increasing speed, pass through a minimum, and then rise again at high speeds as material becomes glasslike in response. Fig 34 Carbon-filled elastomers are twice as large as for unfilled materials –Reinforced material wear away faster due to intrinsic tear strength not being very high for unfilled materials.