Experiment #1 Tension Test

Stress VS Strain of Ductile Material

Exp. 1. Tension Test of Metals - One of the most fundamental concepts in mechanics of materials is the stress-strain behavior of a prismatic bar under tension. An extensive amount of information about the mechanical properties of the material is obtained by this test. ( from Gere)

Exp. 1: Tension Test of Metals Objectives : 1. To obtain the stress-strain curve of a metal (steel) for the full range of loading from zero to rupture. 2. To evaluate some main mechanical properties of steel: proportional limit, yield stress, ultimate stress, modulus of elasticity, percent elongation, percent reduction in cross sectional area, modulus of resilience and toughness 3. Compare reference values to experimental findings 4. To verify the validity of two basic theories and equations: I. Hooke's law: Stress = Modulus of Elasticity * Strain II. Axial elongation equation: Elongation = (Force*Length) (Modulus of Elasticity*Area) 5. Observe characteristics of tensile failures

Brittle VS Ductile Fractures can be generalized into two modes: Ductile failure (most metals) Extensive plastic deformation before fracture. Exhibits necking. Defined Yield stress Rupture does not usually occur at ultimate stress Brittle failure (ceramics, ice, some metals) Relatively little plastic deformation. Crack propagates rapidly without increase in applied stress-Sudden brakes. Rupture usually takes place at the ultimate load.

Exp. 1: Tension Test of Metals Proportional limit (point A) : where the linear stress-strain relationship ends. Proportional Limit (Elastic Limit) is the Max stress that can be applied, that when unloaded the material will return to its original length without causing permanent damage.  Only in this region is Hooke’s law applicable : E, the modulus of elasticity, is the slope of the σ–ε curve in the linear elastic region. The axial elongation equation is also applicable only in this region: stress (σ) A σpl E O εpl strain (ε)

Exp. 1. Tension Test of Metals Yield Stress (point B): the stress at which a material begins to plastically deform. The yield strength of a material is one of the critical parameters used in most engineering designs. Once loading is applied past the elastic limit (point A) permanent damage is induced resulting in residual strain or permanent deformation when unloaded. Directly proportional to cross sectional area Non-ductile or brittle material usually do not exhibit a well defined yield point stress (σ) B σy A O εy strain (ε)

Exp. 1. Tension Test of Metals Yield Strength (point B): For materials with a gradual transition from a straight line to a curve The yield strength is the stress that will cause a specified permanent set of 0.2% 0.2% is a way of writing 0.002in/in In order to find this mark a point on the strain axis at the permanent set (0.2%). Draw a line that is parallel to the initial Elastic Modulus line. Where this line intersects the stress-strain diagram is the yield strength.

Exp. 1. Tension Test of Metals Ultimate Stress (point D): the maximum stress that a material can withstand. Portion BC is called “Perfect Plasticity or Yielding Zone” Portion CD is called “Strain Hardening Zone” Brittle materials: rupture usually occurs at ultimate stress Ductile materials: rupture usually occurs after stress (σ) D σul B A C When the stress keeps on increasing beyond the yield point, the metal becomes stronger and more difficult to deform: More and more stress is required to produce additional plastic deformation. This means that the metal becomes stronger when the stress increases, this is called “Strain Hardening” O εul strain (ε)

Exp. 1. Tension Test of Metals Rupture Strength (point E): stress developed in a material at rupture. It is not necessarily equal to ultimate strength. -Portion DE is called “Necking Zone” -Diameter decreases due to local instability called necking -After necking has begun, lower loads are sufficient to continue elongation until rupture occurs stress (σ) D σf E B A C Necking: strain is large in a specific area, the neck εf O strain (ε)

Exp. 1. Tension Test of Metals Fracture (Rupture) Fracture is the separation of a body into two or more parts. Two modes of fracture are possible, ductile or brittle. The classification is based on whether the material can sustain substantial plastic deformation. Highly ductile material Moderately ductile material Brittle material (a) (b) (c) ( from Callister )

Schematic stress-strain curve for a ductile and a brittle material Exp. 1. Tension Test of Metals brittle ductile Ultimate Stress Schematic stress-strain curve for a ductile and a brittle material

Exp. 1. Tension Test of Metals Resilience : The strain energy density at yield is known as the resilience modulus. Resilience is the capacity of a material to absorb energy elastically upon loading. Mathematically, this can be expressed as : The modulus of resilience (Ur) represents the energy per unit volume that the material can absorb without yielding. stress (σ) B σy A1 O εy strain (ε)

Exp. 1. Tension Test of Metals   stress (σ) σf E A2 εf O strain (ε)

Exp. 1. Tension Test of Metals Tension Test Specimen Materials: AISI 1018 Cold Rolled Steel A36 Hot Rolled Steel Aluminum Lsp= 10 in. (warning: this is not the “L” that is used in the calculations)

Exp. 1. Tension Test of Metals grips extensometer

L is the gauge length of the specimen Exp. 1. Tension Test of Metals L=1” L is the gauge length of the specimen

Exp. 1. Tension Test of Metals To sum up :  materials : AISI 1080 hot rolled steel A36 Hot Rolled Aluminum  diameters: determined in the lab  L=1 in.  loading rate : 200 lb/sec  recording rate : 5 point/ 1 sec References: Text Chapter 3, pages 47-58 Lab manual

Exp. 1. Tension Test of Metals Thank you ! Question?