Flint, marble, and hardstone.
Struck flint shows conchoidal (shell-like) fracture, a bulb of percussion, and ripples radiating from the strike point — the signatures of deliberate working. Frost-shattering and plough damage produce flat or irregular breaks without that bulb.
Marble and limestone sculpture weather differently; note tool marks (point, claw, rasp) and any surviving polish or paint. Traces of pigment in protected hollows are precious — record them and leave them alone.
Tools in tougher stones — granite, basalt, greenstone — were pecked and then ground smooth rather than flaked, so look for shallow peck-marks under the polish. Hardstone intaglios and cameos were carved with abrasives; look for the tell-tale rounded cuts of wheel engraving.
Name the stone cautiously. “Fine-grained dark stone” is honest; a firm geological identification usually needs a specialist, and the record should say which you have.