TRUE STRESS AND STRAIN - PDF Free Download

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

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

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

True M Corrected Stress M Engineering Necking point Strain

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 0.26 530 77,000 (annealed) Alloy steel 0.15 640 93,000 (Type 4340, annealed) Stainless steel 0.45 1275 185,000 (Type 304, annealed) Aluminum (annealed) 0.20 180 26,000 Aluminum alloy 0.16 690 100,000 (Type 2024, heat treated) Copper (annealed) 0.54 315 46,000 Brass 0.49 895 130,000 (70Cu 30Zn, annealed) Sou ce K

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

POLYMERS 60 A 50 Stress (MPa) 40 30 20 B A is a brittle polymer B is a plastic C is highly elastic its an elastomer 10 C 0 0 1 2 3 4 5 6 7 8 Strain

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

A LOOK IN TO WHY THESE MATERIALS ARE DIFFERENT 80 70 4 C (40 F) 12 10 Stress (MPa) 60 50 40 30 20 10 20 C (68 F) 30 C (86 F) 40 C (104 F) 50 C (122 F) 60 C (140 F) To 1.30 8 6 4 2 Stress (10 3 psi) 0 0 0 0.1 0.2 0.3 Strain

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

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

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

ROCKWELL HARDNESS Rockwell and Diamond 120 60 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.

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.

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 15 30 45 15 30 45 15 30 45 80 HRB Represent a hardness of 80 on the B scale

10,000 10 Diamond HARDNESS 5,000 2,000 1,000 80 Nitrided steels 9 8 Corundum or sapphire Topaz 1000 800 600 400 500 110 60 40 Cutting tools File hard 7 6 5 Quartz Orthoclase Apatite For cast iron, steel and brass 300 200 100 Knoop hardness 200 100 50 100 80 60 40 20 0 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

HOWEVER Rockwell hardness 60 70 80 90 100 HRB 20 30 40 50 HRC 250 Different materials Have different relations ships between hardness and Tensile strength 1500 200 Tensile strength (MPa) 1000 Steels 150 100 Tensile strength (10 3 psi) 500 Brass Cast iron (nodular) 50 0 0 0 100 200 300 400 500 Brinell hardness number

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

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

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

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

ba a

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

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

Stage II Stage I

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

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

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)

PHASE DIAGRAMS 100 200 80 Solubility limit Temperature ( C) 60 40 Liquid solution (syrup) Liquid solution + solid sugar 150 100 Temperature ( F) 20 50 Sugar 0 0 20 40 60 80 100 Water 100 80 60 40 20 0 Composition (wt%)

Composition (at% Ni) 0 20 40 60 80 100 1600 2800 1500 Liquid 1453 C 1400 2600 Temperature ( C) 1300 Liquidus line B + L Solidus line 2400 Temperature ( F) 1200 2200 1100 1085 C A 2000 1000 0 20 40 60 80 100 (Cu) Composition (wt% Ni) (a) (Ni)

1300 Liquid Temperature ( C) Tie line B + Liquid 1200 + Liquid R S 20 30 40 50 C L C 0 C Composition (wt% Ni) (b)

Tensile strength (MPa) 400 300 60 50 40 Tensile strength (ksi) 200 0 (Cu) 20 40 60 80 100 (Ni) Composition (wt% Ni) 30 (a) F 10.5

COPPER SILVER Composition (at% Ag) 1200 0 20 40 60 80 100 2200 A Liquidus 2000 1000 Solidus Liquid 1800 F Temperature (C) 800 600 + L + L B 779C (T E ) E 8.0 71.9 91.2 (C E ) (C E ) (C E ) G 1600 1400 1200 Temperature (F) Solvus 1000 400 + 800 C H 600 200 0 20 40 60 80 400 100 (Cu) F 10.6 Composition (wt% Ag) (Ag)

IRON-IRON CARBIDE 1600 0 5 1538 C 1493 C Composition (at% C) 10 15 20 25 1400 L 2500 1394 C + L 1200 1147 C Temperature ( C) 1000 912 C, Austenite 2.14 4.30 + Fe 3 C 2000 Temperature ( F) 800 + 727 C 1500 0.76 600 0.022, Ferrite + Fe 3 C Cementite (Fe 3 C) 1000 400 0 1 2 3 4 (Fe) Composition (wt% C) F 10.26 5 6 6.7 0

1100 1100 1000 900 x + Fe 3 C 1000 900 M c y + Fe 3 C Temperature ( C) 800 700 + a b 727 C Temperature ( C) Te 800 700 d e N f O Pearlite 600 500 + Fe 3 C Fe 3 C 600 500 Fe 3 C Eutectoid + Fe 3 C Proeutectoid 400 x 0 1.0 2.0 Composition (wt % C) 400 0 1.0 2.0 C 0 y Composition (wt % C)