What Is the Relationship Between a Materials Penetration Hardness and Its Ultimate Tensile Strength?

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I discovered a really good article that talks about Mechanical Engineering from a different perspective. Make sure you go over this article and let me know what you think. Today’s article is titled title and you can find the entire article reproduced below for convenience:
Please explain this considering i am just a second year IE student
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Categories: Strength Of Materials Between, Hardness, Materials, Penetration, Relationship, Strength, Tensile, Ultimate
The two are loosely related. Generally the higher UTS of a material the higher the impact resistance it will have. This relationship is near proportional for homogeneous materials. Surface treatments such as shot pening or tempering will change this relationship.