ANS:B - within the core.

In the context of fatigue crack initiation in nitrided machine parts, the phrase "within the core" typically refers to the interior or bulk of the material, away from the surface. When a component is nitrided, the surface undergoes a process where nitrogen diffuses into the material, creating a hardened layer. This surface hardening improves wear resistance and can also enhance fatigue strength by providing a tough outer layer. However, if the nitriding process is not properly controlled, or if there are defects in the material, such as inclusions or voids within the core, fatigue cracks can initiate from these internal imperfections. These cracks may propagate through the core of the material under cyclic loading conditions, leading to failure. In summary, if fatigue cracks originate "within the core" of nitrided machine parts, it suggests that the cracks initiate from internal defects or imperfections in the material, rather than from the surface where the nitriding treatment has been applied.