The manufacturer of a product that is subjected to repetitive cycles has specified that the product should be removed from service when any crack reaches 15% of the critical crack length required to cause fracture. consider a crack that is initially 0.02 mm long in a material with a fracture toughness of 55 mpa √m . the product is continuously cycled between compressive and tensile stresses of 300 mpa at a constant frequency. assume external cracks for which f = 1.12. the materials constants for these units are n = 3.4 and c = 2 × 10-11.
(a) what is the critical crack length required to cause fracture?
(b) how many cycles will it take for the product to be removed from service as specified by the manufacturer,
(c) assuming the specifications were not followed, how many cycles will it take for product to fail? (2+3+3 = 8 points)
answer & explanation:
"the force on a cutting tool are 2600n vertically downward" sounds a little unusual, since most of the time, the tool is above the object to be cut in such a way that the force acting "on the tool" is upwards. we will accept the statement as it is (downwards).
since the two forces are acting at right angles to each other, the resultant can be found using pythagoras theorem, namely
resultant = sqrt(2600^2+2100^2) = 3342 n (approx.)
the angle can be found using the arctangent function, or
angle = arctangent(2600/2100) = 51.07 degrees below the horizontal, since the 2600 n force is acting downwards.
d is the answer
on/off components of a pid controlled accumulates the error over time and responds to system error after the error has been accumulated.
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