Compare strengths: for brittle materials, the compressive strength is generally how related to the tensile strength?

Introduction / Context:
Brittle materials such as cast iron, concrete, ceramics, and some hard polymers exhibit markedly different behavior in tension versus compression. Understanding this asymmetry guides safe design and choice of failure criteria.

Given Data / Assumptions:

• Brittle, low-ductility materials with limited plastic deformation.
• Quasi-static loading conditions.
• Uniform specimens and standard testing procedures.

Concept / Approach:
Brittle materials fail by crack initiation and propagation. In tension, microscopic flaws open and grow, leading to low tensile strength. Under compression, crack faces tend to close, friction and confinement improve resistance, and other failure modes (shear, microcracking) govern at higher loads, resulting in higher compressive strength.

Step-by-Step Solution:

Verification / Alternative check:
Review material datasheets: e.g., gray cast iron and concrete consistently show f_c much greater than f_t, confirming the general rule.

Why Other Options Are Wrong:
“Equal” or “less than” contradict empirical evidence.“Half of” is not a general rule and varies widely by material and microstructure.“Unrelated” ignores tested correlations and mechanisms.

Common Pitfalls:
Applying ductile metal intuition (where tensile and compressive yield strengths are similar) to brittle materials; ignoring flaw sensitivity in tension.

Final Answer:

greater than