M ATERIALS E NGINEERING – D AY 3 Quick Review of Hardness & Hardness Testing Big problem: when ductile materials go brittle… Impact Testing Ductile to Brittle Transition Temperature Introduction to Fracture. See how far we get.

R EVIEW What is the most common type of material test? What does it measure?

S TRESS C ONCENTRATION What is it? Changes in geometry (holes, fillets, threads, notches) can cause local increases in stress (stress raisers) For example: Near a small hole in a large plate, the stress at the edge of the hole is three times as high as the stress away from the hole.

M ORE ON S TRESS C ONCENTRATION F ACTOR Importance: 1. high-strength, low ductility materials can crack 2. cyclic stress coupled with stress concentration is typical for fatigue failures Quantifying: Stress Concentration Factor, K=  max /  nominal where: K is from published charts  nominal is the stress ignoring the stress concentration  max is the highest local stress due to the concentration

W HEN “G OOD ” MATERIALS GO “B AD ” The Schectady. Here is the result.Here is the result These points need mentioning: 1. Steel in the vessel had performed well in tension and hardness testing in non-service environment. 2. Many, many ship failures of this type took place in WWII. Here’s another. The John. P Gaines.Here’s another 3. The Navy had to change material specifications. There was a major research effort. Here’s one result.

T EST TO M EASURE N OTCH T OUGHNESS The following factors affect toughness 1. Tri-axial stress state 2. Presence of a notch or stress concentration 3. Cold Temperature Therefore, a test was designed to probe the materials performance under these more demanding conditions.

C HARPY AND I ZOD T ESTS Specimen Test Apparatus Result: Notch toughness

C HARPY T EST Measures the energy to break, usually of a notched specimen

D UCTILE TO B RITTLE T RANSITION T EMPERATURE There are several ways of specifying the actual temperature at which transition occurs. One is the highest temp on the lower shelf. Another the temp ½ way between the two shelves. Where was the SS Schnectady?

Effect of Radiation on Charpy Energy

Cup-and-cone fracture surface of duralumin as a result of failure by necking. The fracture surface of this Charpy impact specimen show that the fracture mode was a mixture of ductile (dull gray) and brittle (shiny, salt and peppery appearance).

metallurgist.com/.../Fractography.htm

croscope/micrographs/failure/brittle- steel.html

I MPACT T ESTING AdvantagesDisadvantages  Determine minimum temperature of use  Finds “notch sensitive” materials  Difficult to apply quantitatively in design  Addresses temperature, not stress or flaw size

F RACTURE M ECHANICS There is another problem, really more severe than a stress concentrator. It is a sharp crack. Clearly, this can make a ductile material act like a brittle material. i.e. sudden, unexpected failure. Since WWII this has been a fertile field of study. It is the science of fracture mechanics which brings together 1. Analytical methods of solid mechanics to calculate stress field around crack 2. Experimental methods to determine resistance to crack propagation

I NTRODUCTORY I DEAS As crack grows, elastic strain energy is released. Call this release rate F. The crack extends, creating a new surface area and perhaps producing plastic deformation. The crack absorbs energy. Call this absorbtion rate G. For a stable crack F < G. (The energy required to grow the crack is not available.) For an unstable crack, F > G. (Extending the crack releases a lot of strain energy, more than that needed to grow the crack) Clearly, the critical condition F = G is of interest.

I NTRODUCTORY E QUATIONS Griffith, the grandfather of fracture mechanics developed the previous ideas mathematically. In WWII, because of the ship failures, Irwin at NRL extended them to write Where G is the strain energy release rate, E is the elastic modulus, a is the crack length, (or ½ length), and  c is the overall stress at which the crack becomes unstable. Later, Irwin and co-workers recast this relationship into the following form.

I NTRODUCTORY EQUATIONS The f’s are functions of . The variable r measures distance from the crack tip. The variable K is called the stress intensity factor.

F RACTURE M ECHANICS flaw size stress (nominal) Geometry factor For notched members, failure occurs when K I(applied)> K I(critical). Importance: Can quantify”strength” of flawed members. Quantifying: Units: ksi  in, MPa  m Advantage: can set inspection standards can use parts with subcritical flaws

Stress Concentration FactorStress Intensity Factor  multiplier of nominal stress  no units  can’t quantitatively predict failure stress  measure of local stress field  units of: ksi  in, MPa  m  can predict failure stress for discovered flaws

S TRESS I NTENSITY The factor Y depends on crack length and geometry. So, an alternate, and more useful way of talking about crack stability is to frame the discussion in terms of the stress intensity as opposed to the critical strain energy release rate. A crack will become unstable when K = K c, a critical value called fracture toughness. The specimen geometry comes in through Y. See Figure 8.13 in the text.

F RACTURE T OUGHNESS Well, fracture toughness, Kc, depends on specimen thickness. But it’s kind of counterintuitive. Think of a plate. A thin plate is in a condition called plane stress. When in-plane stress is applied, the plate can easily contract in the out-of-plane direction. The corresponding out of plane normal stress and shear stresses are zero. But in a thick plate, the bulk of the material inhibits this out of plane contraction. When it’s thick enough we have plane strain, in which we have three non-zero principal stresses, but zero out of plane strain.

P LANE STRAIN FRACTURE TOUGHNESS As the specimen gets thicker, fracture toughness diminishes, until, in plane strain, it finally becomes constant, that is geometry independent. It can now be regarded as a material property. This material property is called plane strain fracture toughness, K Ic. Failure occurs by yielding takes place when Failure occurs by fracture when

E XAMPLE P ROBLEM A large, thick plate is fabricated from a steel alloy that has a plane strain fracture toughness of 55 MPA m 1/2. If, during service, the plate is exposed to a tensile stress of 200 MPA, determine the minimum length of a surface crack that would lead to failure? Ans. About 24 mm.