I think you are conflating strength and stress here. The material strength (tensile and yield) is the same no matter how thick or thin the geometry. As strength is thought of in terms of load/area, you would effectively have increased applied stress 4 times with the 1" plate in this example compared to the 4" plate. You have to compare this stress (as a starting point) to the material yield and tensile strengths to see if it might be acceptable.

The material properties are related to the size that it was during the last thermo-mechanical process.
If there is a de-rate on 4" plate, then you stuck with that regardless of how thin you machine it.
The properties are related to heat treatment response usually.

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P.E. Metallurgy, consulting work welcomed

The material strength (tensile and yield) is the same no matter how thick or thin the geometry. - nope, completely wrong. See MMPDS tables for strength vs plate thickness.

And agree, you must use properties for the starting plate or bar thickness prior to machining. And you must pay attention to L, LT, and ST direction strength differences.

I'm acronym challenged: what is MMPDS?

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

MMPDS => Metallic Materials Properties Development and Standardization

MMPDS is an FAA/DoD authoritative source for aerospace-use metals [alloys/temper/spec] mechanical [and some physical] data. This manual was an evolution/replacement-for MIL-HDBK-5 Metallic Materials and Elements for Aerospace Vehicle Structures ... which was an evolution/replacement for ANC-5 Strength of Metal Aircraft Elements

ASMH => Aerospace Structural Metals Handbook is also an authoritative source for metal [alloys/temper/spec] mechanical and physical and [some] fabrication data.

DO NOT CONFUSE these FAA/DoD authoritative metals Handbooks with the informative ASM [American Society of Materials] Metals Handbooks

NOTE1. Another useful authoritative handbook for conventional [industrial] metal alloys, mechanical and physical properties, is...
CINDAS Structural Alloys Handbook.

Regards, Wil Taylor
o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation, Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

The MMPDS is maintained by Battel Columbus.
The design properties are based on detailed statistical analysis.
This is why they are picky about starting size and orientation.

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P.E. Metallurgy, consulting work welcomed

Thanks!
(I'm also aerospace deficient; my world is heavy metals)

"Everyone is entitled to their own opinions, but they are not entitled to their own facts."

The strength of the machined part is a function of the original thickness of the plate. So if you machine a part from a 4 inch thick plate of 7075-T73 so that the walls are 1 inch thick or less, the strength of that wall is still that of the 4 inch thick plate you started with (accounting for the various debits due to machining method, notches, surface finish, etc.)

Doug