TRUE STRESS AND STRAIN

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2 TRUE STRESS AND STRAIN TS M F Implies the material is getting weaker? Stress True stress Strain

3 TRUE STRAIN True strain of system Assuming no volume change i.e.

4 RELATION BETWEEN TRUE STRESS AND STRAIN Stress Strain These are only valid to the onset of necking After that measurements at each point must be taken

5 True M Corrected Stress M Engineering Necking point Strain

6 SIMPLE MODEL In some metals and alloys the true stress strain curve past the plastic point can be modelled / fitted to; Several Alloys Material n MPa psi Low-carbon steel ,000 (annealed) Alloy steel ,000 (Type 4340, annealed) Stainless steel ,000 (Type 304, annealed) Aluminum (annealed) ,000 Aluminum alloy ,000 (Type 2024, heat treated) Copper (annealed) ,000 Brass ,000 (70Cu 30Zn, annealed) Sou ce K

7 EXAMPLE A cylindrical specimen of steel having an original diameter of 12.8 mm is tensile tested to fracture and found to have an engineering fracture strength σf of 460 MPa. If its cross-sectional diameter at fracture is 10.7 mm, determine: (a)the ductility in terms of percent reduction in area. (b)the true stress at fracture. 30% 660 MPa

8 POLYMERS 60 A 50 Stress (MPa) B A is a brittle polymer B is a plastic C is highly elastic its an elastomer 10 C Strain

9 THE YIELD POINT TENSILE STRENGTH FOR PLASTIC MATERIALS TS y Stress The modulus and ductility are measured in the same way as for metals For plastic polymers (B) the Yield Point is taken as the maximum point just beyond the linear section of the elastic region. The tensile strength is taken as the stress at fracture Strain

10 A LOOK IN TO WHY THESE MATERIALS ARE DIFFERENT C (40 F) Stress (MPa) C (68 F) 30 C (86 F) 40 C (104 F) 50 C (122 F) 60 C (140 F) To Stress (10 3 psi) Strain

11 By Michael Sepe from Michael P. Sepe LLC From: Plastics Technology Issue: October 2011

12 HARDNESS The ability of a material to resist localised plastic deformation. Originally comparison between materials (how easy was it for A to damage B). Mohs scale. 1 for Talc 10 for Diamond

13 HARDNESS TEST Most common form of mechanical measurement Cheap and no specific specimen needed Non destructive Other engineering quantise can be derived from it such as tensile strength

14 ROCKWELL HARDNESS Rockwell and Diamond kg Superficial cone 100 kg Rockwell Rockwell,,, in. 150 kg diameter 15 kg steel spheres 30 kg Superficial Rockwell 45 kg a r t r ss f r l s giv, P t li l is i g, w il,,, l r ll i.

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16 The most common form of harness test is the Rockwell harness test, In this test as with nearly all harness test an indenter is used to deform (damage) a material. The depth the indenter penetrates determines the harness of the material. There are several Rockwell harness scales and these depend on the shape and size of the indenter with the amount of force used to produce the indent. The Rockwell test uses steel spheres of diameters 1/16, 1/8, 1/4, 1/2 of an inch along with a diamond cone which is used for very hard materials. There are two types of Rockwell test, the Rockwell and the superficial Rockwell. The loads used for the Rockwell are 10 Kg for soft materials and 60, 100 and 150 Kg for harder materials. The loads used for the superficial are 3 Kg, 15 Kg, 30 kg, 45 Kg. These being assigned the numbers X, N, T, W. When a Rockwell test is performed a number and a letter are assigned to the material. The letter defines the test that was performed and a number which defines the harness of that material on the scale. The number ranges from 0-120, however <20 and >100 the scale overlaps with the previous and next scale, so that materials could be measure on two different scales. It is always best to use the scale which delivers a value in the mid range and this is the most accurate. The Rockwell scales can be used on materials from Metals to plastics. Some care needs to be taken when applying the tests. The sample must be thick enough to allow for all of the indentation to be expressed in the upper region of the sample. The spreading of any defects caused by the indentation must not reach the bottom surface, to insure this the sample must be 10x thicker than the indentation. The sample should be smooth and a distance of more than three indentation lengths should be left between the indentation are and sample edges or ridges.

17 Table 7.5a Rockwell Hardness Scales Scale Symbol Indenter Major Load (kg) A Diamond 60 B in. ball 100 C Diamond 150 D Diamond 100 E in. ball 100 F in. ball 60 G in. ball 150 H in. ball 60 K in. ball 150 Table 7.5b Superficial Rockwell Hardness Scales Scale Symbol Indenter Major Load (kg) 15N 30N 45N 15T 30T 45T 15W 30W 45W Diamond Diamond Diamond in. ball in. ball in. ball in. ball in. ball in. ball HRB Represent a hardness of 80 on the B scale

18 10, Diamond HARDNESS 5,000 2,000 1, Nitrided steels 9 8 Corundum or sapphire Topaz Cutting tools File hard Quartz Orthoclase Apatite For cast iron, steel and brass Knoop hardness Rockwell B 20 0 Rockwell C Easily machined steels Brasses and aluminum alloys 4 3 Fluorite Calcite 20 Most plastics 2 Gypsum 10 5 Brinell hardness 1 Talc Mohs hardness

19 HOWEVER Rockwell hardness HRB HRC 250 Different materials Have different relations ships between hardness and Tensile strength Tensile strength (MPa) 1000 Steels Tensile strength (10 3 psi) 500 Brass Cast iron (nodular) Brinell hardness number

20 8 LECTURES 1 on Failure 2 on Phases 3 on Diffusion 2 on liquids

21 F w ( n p A a very ductile fracture B a ductile fracture C a brittle fracture (a) (b) (c)

22 (a) (b) (c) Fibrous Shear (d) (e)

23 STRESS CONCENTRATION 0 m t a Stress X X x 2a x 0 x x (a) 0 Position along X X (b)

24 ba a

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27 Fibrillar bridges Microvoids Crack (a) F 9.17 (b)

28 FATIGUE max Tension + Stress Compression 0 min Time (a) max a Stress Tension Compression + 0 min m Time (b) r DeHavilland Comet Stress Tension Compression + Time

29 Stage II Stage I

30 Zero Comp Max Compres small Compres (a) (d) Small Tensile (b) (e) Max Compres Max Tensile Small Tensile (c) (f)

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32 NOTICE SAME A 2 > 1 1 Crack length a a 1 2 da dn a 1, 2 da dn a 1, 1 a 0 Cycles N

33 da Fatigue crack growth rate, (log scale) dn da dn = A( K) m Region I Nonpropagating fatigue cracks Region II Linear relationship between log K and log da dn Region III Unstable crack growth Stress intensity factor range, K (log scale)

34 PHASE DIAGRAMS Solubility limit Temperature ( C) Liquid solution (syrup) Liquid solution + solid sugar Temperature ( F) Sugar Water Composition (wt%)

35 Composition (at% Ni) Liquid 1453 C Temperature ( C) 1300 Liquidus line B + L Solidus line 2400 Temperature ( F) C A (Cu) Composition (wt% Ni) (a) (Ni)

36 Composition (at% Ni) Liquid 1453 C Temperature ( C) 1300 Liquidus line B + L Solidus line 2400 Temperature ( F) C A (Cu) Composition (wt% Ni) (a) (Ni)

37 1300 Liquid Temperature ( C) Tie line B + Liquid Liquid R S C L C 0 C Composition (wt% Ni) (b)

38 Tensile strength (MPa) Tensile strength (ksi) (Cu) (Ni) Composition (wt% Ni) 30 (a) F 10.5

39 COPPER SILVER Composition (at% Ag) A Liquidus Solidus Liquid 1800 F Temperature (C) L + L B 779C (T E ) E (C E ) (C E ) (C E ) G Temperature (F) Solvus C H (Cu) F 10.6 Composition (wt% Ag) (Ag)

40 IRON-IRON CARBIDE C 1493 C Composition (at% C) L C + L C Temperature ( C) C, Austenite Fe 3 C 2000 Temperature ( F) C , Ferrite + Fe 3 C Cementite (Fe 3 C) (Fe) Composition (wt% C) F

41 x + Fe 3 C M c y + Fe 3 C Temperature ( C) a b 727 C Temperature ( C) Te d e N f O Pearlite Fe 3 C Fe 3 C Fe 3 C Eutectoid + Fe 3 C Proeutectoid 400 x Composition (wt % C) C 0 y Composition (wt % C)