ME 207 Material Science I

Transcription

1 ME 207 Material Science I Chapter 4 Properties in Bending and Shear Dr. İbrahim H. Yılmaz Automotive Engineering Adana Science and Technology University

2 Introduction Many machine and structural parts are often subjected to bending and shear stresses. In most cases, it is highly desirable to test such parts under the conditions that simulate the actual service loading. Static bending and shear properties of materials are not of the same interest as static tension and compression properties. Such properties might be determined directly, or some insight may be gained from tensile test data (e.g., shear yield strength of a material is approximately equal to half of its yieldstrengthintension: S sy S y / 2). The preparation and adequate testing of tension test specimens might be difficult, hence simpler shear and bending tests are often employed. 1

3 Behaviour of Materials in Bending When a member is subjected to bending load, it acts as a beam with a primary function of resisting this loading. In bending, both tensile and compressive stresses are induced over a cross section of the beam. Thus, bending tests are less severe than tensile tests, but more severe than compressive tests. M In fact, bending test does not provide extra information on mechanical behaviour of a material unless bending causes special failure. Its value is defined as a direct means of evaluating behaviour of beams under loading to determine strength and ductility. M Since the loads required to cause failure are relatively small and easily applied, bending tests can be made with simple and cheap apparatus. Test specimens are simple and easy to prepare. Gripping problems are eliminated and deflection data are easily obtained. 2

4 Bending Tests There are two common types of bending tests: a) 3-point bending (Fig. 1a): applying a concentrated load at the span centre. b) 4-point bending (Fig. 1b): applying half-loads equally distant from supports. 3-pointbendingmethod is often used due to its simplicity. On the contrary,4-point bending (pure-bending) method provides better material characteristics due to the constant bending moment which occurs between inner load points. Figure 1a 3 beam 1 2 Figure 1b 3 4 beam L 1 2 L a a P L P/2 P/2 a L a 3

5 Bending Tests Bending tests are intended for brittle materials when scope of test istodetermine the bending strength of material. Thus, such tests are notably employed for cast iron (based on ASTM A48) as well as concrete, wood and certain plastics (according to ASTM D790-66, BS 2782 and DIN 53452) using circular or rectangular specimens. To determine bending strength,beammustbeproportionedsothatitwillnotfailin shear or by lateral deflection before reaching its ultimate flexural limit. Usually, long specimens of high length-to-depth ratio (L/h > 10) are used. Shorter beams (L/h < 6) are intended for shear failure testing in bending. 3-point bending test 4-point bending test 4

6 Bending Strength Bending strength is also known as:flexuralstrength,cross-breakingstrength, transverse strength, modulus of rupture, and coefficient of bending strength. Bending strength of brittle materials obtained from bending tests would be greater than that from tensile tests. As approaching failure,neutral axis shifts toward compression face(by distance ofc), which tends to strengthen the beam. N. A. c M For a rectangular part in 3-point bending test, bending strength is the highest stress at moment of rupture: max M c 3 F L I 2 wh 2 M : bending moment I : area moment of inertia c : distance from neutral axis F : load at span center L : distance between supports w : width of specimen h : thickness of specimen 5

7 Stiffness in Bending Stiffness in bending is the resistance to deformation in bending within elastic range. A measure of this property is modulus of elasticity in bending defined by load-deflection diagram (Fig. 2). Load-deflection measurements are carried out using 3-point bending test, and hence elastic modulus in bending is definedfromstraightportionofcurve. F load F Figure 2 d d deflection Deflection is dependent upon not only the material but also the configuration of cross-section and unsupported length. Hence, stiffness in bending for identical specimens to be tested under identical conditions can be compared. d max FL Ebend 48 EI 4 FL 3 wh d 3 3 F : load at the straight portion of curve d : deflection corresponding to load L : distance between outer supports w : width of specimen h : thickness of specimen 6

8 Cold-Bend Tests Bending tests cannot be employed to determine bending strength of ductile materials as they can be fully bent without rupture. For ductile materials, cold-bend and folding tests are applied to determine whether they can be bent sharply without cracking. The scope is to check ductility for a particular type of service or to detect loss of ductility under certain types of treatment. The test involves sharp bending of a bar through a large angle and noting if cracking occurs on the outer surface. The aim is to determine the angle ( ) at which cracking starts (Fig. 3a). If no cracks produced while specimen is bent around the pin, testing is continued by compressing the specimen on itself between the compression platens referred as folding (Fig. 3b). Such tests are used for testing special parts: structural steels (ASTM A36-74), boiler rivet steels and rivets (ASTM A141), pressure vessel plates (ASTM A285-72). Figure 3 ( a ) ( b ) h 7

9 Cold-Bend Tests Minimum ductility that must be possessed by a material is defined by Tetmajer s bending limit (Bg). Pin diameters and the corresponding bending limits are given in table below: Bg 50h r h : thickness of specimen r : folding radius (Fig. 3a) D 0 0.5h 1.0h 1.5h 2.0h 2.5h 3.0h Bg point bending test of ductile flat specimens (30-50 mm wide) is covered in DIN Bending load is applied slowly and steadily, and the ductility is defined as angle ( ) until which specimen can be bent without cracking on the tension side (Fig. 4). The inner distance between D+3h supports should be D+3h, and D the supports must have a radius of 25 mm (for h < 12 mm) and 50 mm (for h > 12 mm). Figure 4 8

10 Special Bend Tests 1. Notched-Bar Test: Used to specify the resistance of a material against shock and its ability to withstand stress concentration. Similar to tension test, the work done in bending the specimen through about a right angle (using Monsanto Tensometer in Fig. 5) can also be employed as toughness index number that is expressed as product of forceappliedbythenoseandthedistancethroughwhichitmoves. Figure 5 9

11 Special Bend Tests 2. Weld Test: Similar in concept to 3-point bending test, weld test is carried out by subjecting a butt-welded specimen to transverse loading in a fixture. The load is applied slowly and steadily until either cracks are produced on the tension side or the specimen is bent to extreme limit in the fixture (in such case, specimen is removed and testing is continued as in folding test). Fig. 6a & 6b show the free-bend test fixtures for testing the ductility of welds according to ASTM E16-64 and DIN 50121, respectively. Figure 6a Figure 6b 10

12 Special Bend Tests 3. Fiber-Strain Measurements: made in connection with weld tests. Tension side of specimen is marked over a distance and percent elongation of outer fiber is specified through the use of flexible tape. Hence, original (L 0 ) and final (L f ) lengths are used to calculate ductility (R): R f L L L Hot-Bend Test: made with specimens heated to red-hot temperature to determine suitability of material to hot-working. This test is also employed for welded joints to test blue brittleness. Plain carbon steels experience discontinuous yielding within C (known as blue brittle region ) as steel heated in this range shows a lower tensile ductility and higher notch sensitivity. Hot-bend test of welded joints is important if the weld seam is going to be subjected to forming operation. 5. Quenched-Bend Test: used in connection with the plates used for boilers. The specimen is heated to 650 C and held at this temp. about half an hour. Then quenched in warm water around 28 C, and subjected to bend test. Aim is to detect traces of nitrogen present in metal, indicated by fracture. 11