Basic fracture mechanics

hello welcome to fracture synopsis 2 we'll have a basic introduction to fracture mechanics all right so the first thing to address is of course what fracture mechanics is all about and we'll remember from synopsis one that fracture involves a crack of some length the length of which increases uh upon uh loading and fr mechanics then is about when uh is about understanding when that crack becomes critical so when the crack gets to a sufficiently long length that the crack propagation goes from being stable to being unstable and uh it turns out that we can describe

uh fracture mechanics um in its basic sense using this equation here and this is something known as the stress intensity factor stress intensity factor and that relates the stress and the uh crack length through this geometric Factor here geometric factor it's just a function of the sample size and the uh size of the crack so this is a very useful equation for us um and it's as I said the basis for fracture mechanics so I think to help understand the stress intensity factor um there's a great a great uh little statement in uh Herzberg this

there an excellent book that he's written on fracture and deformation anyway the statement is at the top of the slide there stress is to strength a stress intensity factor is to fracture toughness so let's just explore that and of course we've seen earlier in in the course uh a stress strain curve and on that stress strain curve we identified a number of points say the the yield strength okay the ultimate tensile strength and the fracture strength and you remember that we called them strength values and strength being a specific value of stress okay specific value

of stress so now we have the stress intensity factor k and a specific value of that is the critical stress intensity factor that is the stress intensity factor when the crack becomes critical the crack is grown to a sufficient length that it um is critical that is the the propagation is now going to become unstable stable and uh more specifically actually we're going to look at the most common um form of the stress intensity factor sorry of the critical stress intensity factor the the plain strain fracture toughness k1c okay and and the the one the

Roman numeral one there actually refers to mode one crack displacement that's crack opening just out of Interest say here crack two uh mode two is is sliding and mode three is referred to as tearing but mode one is what we're are going to be interested in that's the most common form of CRA crack displacement that we'll encounter and so the um K1 C is the fracture toughness and remember that the fracture toughness is a specific value of stress intensity factor so the last thing I'd like to uh just address is this clarification we've covered a

number of things here um stress concentration factor which was covered in the synopsis number one you'll remember was um K subt that's the stress concentration Factor at the crack tip and that was just the ratio of the maximum stress at the tip of a elliptical crack in in our case uh to the applied stress okay so stress concentration Factor how much is the stress concentrated and now we've uh also earlier in the year seen this this um property of the toughness and we Define the toughness as the area under the stress string curve up to

fracture okay so that's the toughness that's essentially how much energy is involved in in breaking and fracturing the sample so it's you know it's somewhat related but it is a different term to this new term that we've just in introduced which was the critical stress intensity factors remember the stress intensity factor k um when it becomes critical the crack grows and we have a specific value of the stress intensity factor under the right conditions which we call the k1c and that's the fracture toughness so it's important to realize that the fracture toughness is different from

toughness which is the area under the curve and k1c is as well different from the stress concentration Factor so stress intensity factor stress concentration factor and toughness are um related but they are each unique and it's important to appreciate that difference so quickly uh fracture mechanics is about understanding uh when a crack becomes critical we have this relationship here for fracture mechanics in fact we saw that the stress intensity factor under specific conditions and when it becomes critical is the known as the fracture toughness and that is a material property okay so that's a function

of the material that you've chosen for the application stress is of course a function of the design or the application and this is the uh crack size and uh that could be something that you determine through non-destructive testing or it could be a function of U an element of the design or your processing uh conditions