The mode of failure in a fillet weld material is shear.

Shear failure occurs when the applied load is parallel to the area of the material. In the case of fillet welds, the load is typically applied parallel to the weld, causing shear stress to develop in the weld material.

Here is a detailed explanation of why shear is the mode of failure in fillet welds:

1. Understanding Fillet Welds:
- Fillet welds are commonly used in structural steel connections to join two pieces of metal at an angle.
- They are often used to provide strength and stability in various applications, such as in the construction of buildings, bridges, and other steel structures.
- Fillet welds are typically triangular in shape and are formed by depositing molten filler metal between the two pieces of metal to be joined.

2. Load Transfer in Fillet Welds:
- In fillet welds, the load is transferred from one member to another through the weld.
- When an external force is applied to the joint, the load is distributed across the fillet weld.
- The load is transferred primarily through shear stress, as the applied load is parallel to the weld.

3. Shear Failure in Fillet Welds:
- Shear failure occurs when the shear stress exceeds the shear strength of the weld material.
- The shear strength of a fillet weld depends on various factors, such as the material properties of the weld metal and the base metal, the size of the weld, and the welding process used.
- If the applied load exceeds the shear strength of the fillet weld, shear failure will occur, resulting in the separation or tearing of the weld material.

4. Other Modes of Failure:
- While shear is the primary mode of failure in fillet welds, other failure modes can also occur depending on the specific conditions.
- Tension failure can occur if the applied load causes the base metal adjacent to the weld to elongate and eventually rupture.
- Bearing failure can occur if the load causes the base metal to deform or crush, resulting in a loss of contact between the two pieces being joined.
- Crushing failure can occur if the weld material or the base metal is subjected to excessive compressive forces, causing it to deform or collapse.

In conclusion, the mode of failure in a fillet weld material is shear. Shear failure occurs when the applied load is parallel to the weld, causing the weld material to separate or tear. While other failure modes can also occur in certain circumstances, shear is the primary mode of failure in fillet welds.